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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis

Functional Analysis (Hardcover, 2nd Revised edition): P.K. Jain, O.P. Ahuja Functional Analysis (Hardcover, 2nd Revised edition)
P.K. Jain, O.P. Ahuja
R1,134 Discovery Miles 11 340 Ships in 12 - 17 working days

Functional Analysis is based on the lecture notes of distinguished authors and is designed to cater to the needs of students who are yet to be exposed to the subject, as well as senior undergraduate- and graduate-level students at universities the world over. The text begins with a preliminary chapter that establishes uniform notations and covers background material in real analysis, linear algebra, and metric spaces. It is followed by chapters on Normed and Banach Spaces, Bounded Linear Operators and Bounded Linear Functional. This text also deals with the concept and specific geometry of Hilbert Spaces, Functional and Operators on Hilbert Spaces, and an Introduction to Spectral Theory. The appendix provides an introduction to Schauder Bases. This is a second edition, written in a more simple and lucid language and illustrated with familiar examples. It is an ideal textbook for easy comprehension of the subject. The clear explanations, numerous examples, problems and illustrative figures also make the text invaluable for self-study and as a reference book.

Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum... Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics (Hardcover)
Willi-Hans Steeb, Wolfgang Mathis
R3,781 Discovery Miles 37 810 Ships in 10 - 15 working days

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

Extremum Seeking through Delays and PDEs (Hardcover): Tiago Roux Oliveira, Miroslav Krstic Extremum Seeking through Delays and PDEs (Hardcover)
Tiago Roux Oliveira, Miroslav Krstic
R3,485 R3,257 Discovery Miles 32 570 Save R228 (7%) Ships in 12 - 17 working days

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find: Numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed. Extensions from single-player optimization to noncooperative games, under delays and pdes, are provided. The delays and pdes are compensated in the control designs using the pde backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory. Accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

A Mathematical Journey to Quantum Mechanics (Hardcover, 1st ed. 2021): Salvatore Capozziello, Wladimir-Georges Boskoff A Mathematical Journey to Quantum Mechanics (Hardcover, 1st ed. 2021)
Salvatore Capozziello, Wladimir-Georges Boskoff
R2,580 Discovery Miles 25 800 Ships in 12 - 17 working days

This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schroedinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.

Bloch-type Periodic Functions: Theory And Applications To Evolution Equations (Hardcover): Yong-kui Chang, Gaston Mandata... Bloch-type Periodic Functions: Theory And Applications To Evolution Equations (Hardcover)
Yong-kui Chang, Gaston Mandata N'G'Uerekata, Rodrigo Ponce
R2,168 Discovery Miles 21 680 Ships in 10 - 15 working days

This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.

Operator Theory and Harmonic Analysis - OTHA 2020, Part I - New General Trends and Advances of the Theory (Hardcover, 1st ed.... Operator Theory and Harmonic Analysis - OTHA 2020, Part I - New General Trends and Advances of the Theory (Hardcover, 1st ed. 2021)
Alexey N. Karapetyants, Vladislav V. Kravchenko, Elijah Liflyand, Helmuth R. Malonek
R6,768 Discovery Miles 67 680 Ships in 10 - 15 working days

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Fractals - Form, Chance and Dimension (Hardcover, Reprint ed.): Benoit B. Mandelbrot Fractals - Form, Chance and Dimension (Hardcover, Reprint ed.)
Benoit B. Mandelbrot
R1,110 Discovery Miles 11 100 Ships in 10 - 15 working days
The Mathematics of Errors (Hardcover, 2021 ed.): Nicolas Bouleau The Mathematics of Errors (Hardcover, 2021 ed.)
Nicolas Bouleau
R3,995 Discovery Miles 39 950 Ships in 12 - 17 working days
A Birman-Schwinger Principle in Galactic Dynamics (Hardcover, 1st ed. 2021): Markus Kunze A Birman-Schwinger Principle in Galactic Dynamics (Hardcover, 1st ed. 2021)
Markus Kunze
R3,969 Discovery Miles 39 690 Ships in 12 - 17 working days

This monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability properties of steady state solutions in galactic dynamics. The opening chapters lay the framework for the main result through detailed treatments of nonrelativistic galactic dynamics and the Vlasov-Poisson system, the Antonov stability estimate, and the period function $T_1$. Then, as the main application, the Birman-Schwinger type principle is used to characterize in which cases the "best constant" in the Antonov stability estimate is attained. The final two chapters consider the relation to the Guo-Lin operator and invariance properties for the Vlasov-Poisson system, respectively. Several appendices are also included that cover necessary background material, such as spherically symmetric models, action-angle variables, relevant function spaces and operators, and some aspects of Kato-Rellich perturbation theory. A Birman-Schwinger Principle in Galactic Dynamics will be of interest to researchers in galactic dynamics, kinetic theory, and various aspects of quantum mechanics, as well as those in related areas of mathematical physics and applied mathematics.

Finite-Dimensional Vector Spaces (Hardcover): Paul Halmos Finite-Dimensional Vector Spaces (Hardcover)
Paul Halmos
R643 Discovery Miles 6 430 Ships in 12 - 17 working days
Theory (Hardcover, 2nd corr. and exten. edition): Steven Lord, Fedor Sukochev, Dmitriy Zanin Theory (Hardcover, 2nd corr. and exten. edition)
Steven Lord, Fedor Sukochev, Dmitriy Zanin
R4,487 Discovery Miles 44 870 Ships in 12 - 17 working days

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Operator Theory - Proceedings of the International Conference on Operator Theory, Hammamet, Tunisia, April 30 - May 3, 2018... Operator Theory - Proceedings of the International Conference on Operator Theory, Hammamet, Tunisia, April 30 - May 3, 2018 (Hardcover)
Aref Jeribi
R4,217 Discovery Miles 42 170 Ships in 12 - 17 working days

This proceedings volume collects select contributions presented at the International Conference in Operator Theory held at Hammamet, Tunisia, on April 30 May 3, 2018. Edited and refereed by well-known experts in the field, this wide-ranging collection of survey and research articles presents the state of the art in the field of operator theory, covering topics such as operator and spectral theory, fixed point theory, functional analysis etc.

Orthogonal Polynomials: Current Trends and Applications - Proceedings of the 7th EIBPOA Conference (Hardcover, 1st ed. 2021):... Orthogonal Polynomials: Current Trends and Applications - Proceedings of the 7th EIBPOA Conference (Hardcover, 1st ed. 2021)
Francisco Marcellan, Edmundo J. Huertas
R4,617 Discovery Miles 46 170 Ships in 10 - 15 working days

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganes, Spain, from July 3 to July 6, 2018.These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields.In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.

Aggregation Operators for Various Extensions of Fuzzy Set and Its Applications in Transportation Problems (Hardcover, 1st ed.... Aggregation Operators for Various Extensions of Fuzzy Set and Its Applications in Transportation Problems (Hardcover, 1st ed. 2021)
Akansha Mishra, Amit Kumar
R3,048 Discovery Miles 30 480 Ships in 10 - 15 working days

This book introduces readers to the fundamentals of transportation problems under the fuzzy environment and its extensions. It also discusses the limitations and drawbacks of (1) recently proposed aggregation operators under the fuzzy environment and its various extensions; (2) recently proposed methods for solving transportation problems under the fuzzy environment; and (3) recently proposed methods for solving transportation problems under the intuitionistic fuzzy environment. In turn, the book proposes simplified methods to overcome these limitations.

Positivity and its Applications - Positivity X, 8-12 July 2019, Pretoria, South Africa (Hardcover, 1st ed. 2021): Eder... Positivity and its Applications - Positivity X, 8-12 July 2019, Pretoria, South Africa (Hardcover, 1st ed. 2021)
Eder Kikianty, Mokhwetha Mabula, Miek Messerschmidt, Jan Harm van der Walt, Marten Wortel
R5,733 Discovery Miles 57 330 Ships in 12 - 17 working days

This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.

Ridge Functions and Applications in Neural Networks (Paperback): Vugar E. Ismailov Ridge Functions and Applications in Neural Networks (Paperback)
Vugar E. Ismailov
R3,392 Discovery Miles 33 920 Ships in 12 - 17 working days

Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.

Scattering Theory for Transport Phenomena (Hardcover, 1st ed. 2021): Hassan Emamirad Scattering Theory for Transport Phenomena (Hardcover, 1st ed. 2021)
Hassan Emamirad
R3,543 Discovery Miles 35 430 Ships in 10 - 15 working days

The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten-von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland's formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schroedinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.

The Rademacher System in Function Spaces (Hardcover, 1st ed. 2020): Sergey V. Astashkin The Rademacher System in Function Spaces (Hardcover, 1st ed. 2020)
Sergey V. Astashkin
R4,361 Discovery Miles 43 610 Ships in 12 - 17 working days

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Direct and Inverse Finite-Dimensional Spectral Problems on Graphs (Hardcover, 1st ed. 2020): Manfred Moeller, Vyacheslav... Direct and Inverse Finite-Dimensional Spectral Problems on Graphs (Hardcover, 1st ed. 2020)
Manfred Moeller, Vyacheslav Pivovarchik
R3,851 Discovery Miles 38 510 Ships in 10 - 15 working days

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology - Ronald G. Douglas Memorial Volume... Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology - Ronald G. Douglas Memorial Volume (Hardcover, 1st ed. 2020)
Raul E. Curto, William Helton, Huaxin Lin, Xiang Tang, Rongwei Yang, …
R4,681 Discovery Miles 46 810 Ships in 10 - 15 working days

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas' students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Dynamical Systems Method for Solving Nonlinear Operator Equations, Volume 208 (Hardcover, 208th edition): Alexander G. Ramm Dynamical Systems Method for Solving Nonlinear Operator Equations, Volume 208 (Hardcover, 208th edition)
Alexander G. Ramm
R4,262 Discovery Miles 42 620 Ships in 12 - 17 working days

The book is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved
in the book, and some of the background material is also included. The results presented are mostly obtained by the author.
- Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed
- Self-contained, suitable for wide audience
- Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes)

Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity (Hardcover, 1st ed. 2020): Alexander A. Lokshin Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity (Hardcover, 1st ed. 2020)
Alexander A. Lokshin
R1,597 Discovery Miles 15 970 Ships in 10 - 15 working days

The objective of this book is to construct a rigorous mathematical approach to linear hereditary problems of wave propagation theory and demonstrate the efficiency of mathematical theorems in hereditary mechanics. By using both real end complex Tauberian techniques for the Laplace transform, a classification of near-front asymptotics of solutions to considered equations is given-depending on the singularity character of the memory function. The book goes on to derive the description of the behavior of these solutions and demonstrates the importance of nonlinear Laplace transform in linear hereditary elasticity. This book is of undeniable value to researchers working in areas of mathematical physics and related fields.

Nonlinear Analysis, Differential Equations, and Applications (Hardcover, 1st ed. 2021): Themistocles M. Rassias Nonlinear Analysis, Differential Equations, and Applications (Hardcover, 1st ed. 2021)
Themistocles M. Rassias
R4,038 Discovery Miles 40 380 Ships in 12 - 17 working days

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers-Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg-Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdos-Renyi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Topology of Infinite-Dimensional Manifolds (Hardcover, 1st ed. 2020): Katsuro Sakai Topology of Infinite-Dimensional Manifolds (Hardcover, 1st ed. 2020)
Katsuro Sakai
R4,368 Discovery Miles 43 680 Ships in 12 - 17 working days

An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk's conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial -manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial -manifold and the Hauptvermutung for them is true.

Graphs and Discrete Dirichlet Spaces (Hardcover, 1st ed. 2021): Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski Graphs and Discrete Dirichlet Spaces (Hardcover, 1st ed. 2021)
Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski
R4,374 Discovery Miles 43 740 Ships in 12 - 17 working days

The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.

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