"Recent Advances in Harmonic Analysis and Applications" features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations.Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations.

Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations. "

The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

This volume contains research articles from the field of Nonlinear Differential Equa tions which result from the "Workshop on Nonlinear Analysis and Applications" held in Bergamo on July 9 to 13, 200l. This workshop was the third edition of a meeting which first took place in Campinas in 1996 and was founded in part upon scientific cooperation, already well initiated, between some participants, on specific problems in Nonlinear Analysis, and in part upon the whish to extend such cooperation to other researchers and to other topics. The scientific collaboration between Italy and Brazil is not new; it dates back at least to the thirties, and includes, among others, the name of Luigi Fantappie, just to mention only one of the earliest Italians that developed part of their scien tific activity in Brazil. If the first workshop had mainly an informal character, the second, which took place in 1998 again in Campinas, already had the structure and the breath of a true international congress. At this point it was the Italians turn to organize the third meeting. The main purpose of the conference was to provide a forum for the discussion of recent work and modern trends in various fields of Nonlinear Analysis. About 130 researchers coming from 17 countries attended the conference."

Symbolic Integration I is destined to become the standard reference work in the field. Manuel Bronstein is a leading expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

This second edition offers a new chapter on parallel integration, a number of other improvements and a couple of additional exercises.

From the reviews of the first edition: ..". The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions " F. Winkler, Computing Reviews 1997 "

This volume is a result of two international workshops, namely the Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, held jointly in Sunne, Sweden from May 1-6 2012. The subject of the inverse problems workshop was to present new analytical developments and new numerical methods for solutions of inverse problems. The objective of the large-scale modeling workshop was to identify large-scale problems arising in various fields of science and technology and covering all possible applications, with a particular focus on urgent problems in theoretical and applied electromagnetics. The workshops brought together scholars, professionals, mathematicians, and programmers and specialists working in large-scale modeling problems. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.

This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity.

It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.

This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

This volume presents a collection of selected papers by the prominent Brazilian mathematician Djairo G. de Figueiredo, who has made significant contributions in the area of Differential Equations and Analysis. His work has been highly influential as a challenge and inspiration to young mathematicians as well as in development of the general area of analysis in his home country of Brazil.

In addition to a large body of research covering a variety of areas including geometry of Banach spaces, monotone operators, nonlinear elliptic problems and variational methods applied to differential equations, de Figueiredo is known for his many monographs and books. Among others, this book offers a sample of the work of Djairo, as he is commonly addressed, advancing the study of superlinear elliptic problems (both scalar and system cases), including questions on critical Sobolev exponents and maximum principles for non-cooperative elliptic systems in Hamiltonian form.

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author's past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

This modern introduction to infinitesimal methods is a translation of the book Metodos Infinitesimais de Analise Matematica by Jose Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.
Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbersIncludes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis"

Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.

During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field.

Key features and topics:

* Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers.

* An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces.

* Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets.

* Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames.

* Content split naturally intotwo parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets.

Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

This book is a useful overview of results in multivariate probability distributions and multivariate analysis as well as a reference to harmonic analysis on symmetric cones adapted to the needs of researchers in analysis and probability theory.

This book adresses the needs of both researchers and practitioners. It combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these models to the risk and portfolio management of interest-rate derivatives. It can also serve as a valuable textbook for graduate and PhD students in mathematics who want to get some knowledge about financial markets. The first part of the book is an exposition of advanced stochastic calculus. It defines the theoretical framework for the pricing and hedging of contingent claims with a special focus on interest-rate markets. The second part covers a selection of short and long-term oriented risk measures as well as their application to the risk management of interest -rate portfolios. Interesting and comprehensive case studies are provided to illustrate the theoretical concepts.

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog's theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz's rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.

During its 2004 meeting in Warsaw the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) decided to support a proposal of the Georgian National Committee to hold in Tbilisi (Georgia), on April 23-27, 2007, the IUTAM Symposium on the Relation of Shell, Plate, Beam, and 3D Models, dedicated to the Centenary of Ilia Vekua. The sci- ti?c organization was entrusted to an international committee consisting of Philipppe G. Ciarlet (Hong Kong), the late Anatoly Gerasimovich Gorshkov (Russia),JornHansen(Canada),GeorgeV.Jaiani(Georgia,Chairman),Re- hold Kienzler (Germany), Herbert A. Mang (Austria), Paolo Podio-Guidugli (Italy), and Gangan Prathap (India). The main topics to be included in the scienti?c programme were c- sen to be: hierarchical, re?ned mathematical and technical models of shells, plates, and beams; relation of 2D and 1D models to 3D linear, non-linear and physical models; junction problems. The main aim of the symposium was to thoroughly discuss the relations of shell, plate, and beam models to the 3D physicalmodels.Inparticular,peculiaritiesofcuspedshells,plates,andbeams were to be emphasized and special attention paid to junction, multibody and ? uid-elastic shell (plate, beam) interaction problems, and their applications. The expected contributions of the invited participants were anticipated to be theoretical, practical, and numerical in character.

This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames.

Contributors: B. Banerjee, D.P. Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curbera, M. Henriksen, A.G. Kusraev, J. Marti-nez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Triki, A.W. Wickstead

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ? u = Au, 2 't 2 where u = u(x, t) is a vector-valued function, x is a point in a domain inR or 3 R, and A is a linear elliptic di?erential operator. To facilitate a better und- standing of these two types of methods, below we propose to illustrate their mechanisms in action on a speci?c mathematical model rather than in a more impersonal abstract setting. For this purpose, we have chosen the hyperbolic system of partial di?erential equations governing the nonstationary bending of elastic plates with transverse shear deformation. The reason for our choice is twofold. On the one hand, in a certain sense this is a hybrid system, c- sistingofthreeequationsforthreeunknownfunctionsinonlytwoindependent variables, which makes it more unusual and thereby more interesting to the analyst than other systems arising in solid mechanics. On the other hand, this particular plate model has received very little attention compared to the so-called classical one, based on Kirchho? s simplifying hypotheses, although, as acknowledged by practitioners, it represents a substantial re?nement of the latter and therefore needs a rigorous discussion of the existence, uniqueness, and continuous dependence of its solution on the data before any construction of numerical approximation algorithms can be contemplated."

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.