This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author's previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability's many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter's contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.

"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --MATHEMATICAL REVIEWS

This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.

Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers-Ulam's stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam's stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers-Ulam stability of a discrete diamond-alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.

Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.

This book collects papers based on the XXXVI Bialowieza Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Bialowieza Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year's lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Bialowieza forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels. The book presents the dynamic of Covid-19 spread behaviour worldwide. It is noticed that the spread dynamic followed process with nonlocal behaviours which resemble power law, fading memory, crossover and stochastic behaviours. Fractional stochastic differential equations are therefore used to model spread behaviours in different parts of the worlds. The content coverage includes brief history of Covid-19 spread worldwide from December 2019 to September 2021, followed by statistical analysis of collected data for infected, death and recovery classes.

This volume highlights the analysis on noncompact and singular manifolds within the framework of the cone calculus with asymptotics. The three papers at the beginning deal with parabolic equations, a topic relevant for many applications. The first article presents a calculus for pseudodifferential operators with an anisotropic analytic parameter. The subsequent paper develops an algebra of Mellin operators on the infinite space-time cylinder. It is shown how timelike infinity can be treated as a conical singularity. In the third text - the central article of this volume - the authors use these results to obtain precise information on the long-time asymptotics of solutions to parabolic equations and to construct inverses within the calculus. There follows a factorization theorem for meromorphic symbols: It is proven that each of these can be decomposed into a holomorphic invertible part and a smoothing part containing all the meromorphic information. It is expected that this result will be important for applications in the analysis of nonlinear hyperbolic equations. The final article addresses the question of the coordinate invariance of the Mellin calculus with asymptotics.

The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.

Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23-25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almeria and the University of Malaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.

This textbook is a concise yet precise supplement to traditional books on Signals and Systems, focusing exclusively on the continuous-time case. Students can use this guide to review material, reinforce their understanding, and see how all the parts connect together in a uniform treatment focused on mathematical clarity. Readers learn the "what", "why" and "how" about the ubiquitous Fourier and Laplace transforms encountered in the study of linear time-invariant systems in engineering: what are these transforms, why do we need them, and how do we use them? Readers will come away with an understanding of the gradual progression from time-domain analysis to frequency-domain and s-domain techniques for continuous-time linear time-invariant systems. This book reflects the author's experience in teaching this material for over 25 years in sophomore- and junior-level required engineering courses and is ideal for undergraduate classes in electrical engineering.

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis - all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Gluck, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernandez, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lu, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Roman, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations.

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schroedinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.