Functional analysis and transforms Books

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis,...

This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on...

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's...

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation...

This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier...

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise,...

The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional...

Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory...

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of...

From the reviews "This is a reprint of the original edition of Lang's 'A First Course in Calculus', which was first published in 1964....The treatment is 'as rigorous as any mathematician would wish it'....[The exercises] are...

There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional...

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of...

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...

A First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authors' own notes on the subject, which they have been teaching since the 1990s. Over the years they have added...

Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read...

It is an indisputable argument that the formulation of metrics (by Fréchet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach's fixed point theorem. Because the underlying space of this...

A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format,...

The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the...

This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus­ tomarily offered as a first or second year graduate course in United States...

The present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of vary­ ing...

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general...

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve...

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in...

This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending...

This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on...

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year...

Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973...

The purpose of this book is to provide the student beginning undergraduate mathematics with a solid foundation in the basic logical concepts necessary for most of the subjects encountered in a university mathematics course. The...

Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid...

In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or...

Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read...

Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering. Operational Calculus and...

This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.

The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func­ tions. Hankel operators can be defined as operators having infinite Hankel...

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as...

The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old...

The history of mathematics is, to a considerable extent, connected with the study of solutions of the equation f(x)=a=const for functions f(x) of one real or complex variable. Therefore, it is surprising that we know very little about solutions of...