Books in Functional analysis

Theory of Approximate Functional Equations

1st Edition
February 23, 2016
Madjid Eshaghi Gordji + 1 more
English
Hardback
9 7 8 0 1 2 8 0 3 9 2 0 5
eBook
9 7 8 0 1 2 8 0 3 9 7 1 7

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.

Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations

1st Edition
November 4, 2015
T Jangveladze + 2 more
English
Hardback
9 7 8 0 1 2 8 0 4 6 2 8 9
eBook
9 7 8 0 1 2 8 0 4 6 6 9 2

This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided.

Nine Introductions in Complex Analysis - Revised Edition

1st Edition
Volume 208
September 6, 2007
Sanford L. Segal
English
eBook
9 7 8 0 0 8 0 5 5 0 7 6 3

The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective.

Infinite Dimensional Linear Control Systems

1st Edition
Volume 201
July 12, 2005
H.O. Fattorini
English
eBook
9 7 8 0 0 8 0 4 5 7 3 4 5

For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date).The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals.The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research.Key features:· Applications to optimal diffusion processes.· Applications to optimal heat propagation processes.· Modelling of optimal processes governed by partial differential equations.· Complete bibliography.· Includes the latest research on the subject.· Does not assume anything from the reader except basic functional analysis.· Accessible to researchers and advanced graduate students alike

Applications of Functional Analysis and Operator Theory

2nd Edition
Volume 200
February 8, 2005
V. Hutson + 2 more
English
eBook
9 7 8 0 0 8 0 5 2 7 3 1 4

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

Functional Equations in Applied Sciences

1st Edition
Volume 199
November 4, 2004
Enrique Castillo + 2 more
English
eBook
9 7 8 0 0 8 0 4 7 7 9 1 6

The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems.An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm.The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications.

Functional Analysis and its Applications

1st Edition
Volume 197
July 30, 2004
Vladimir Kadets + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 2 8 0 5

The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach ƒ{ the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.

Sobolev Spaces

2nd Edition
Volume 140
June 26, 2003
Robert A. Adams + 1 more
English
Hardback
9 7 8 0 1 2 0 4 4 1 4 3 3
eBook
9 7 8 0 0 8 0 5 4 1 2 9 7

Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.

Recent Progress in Functional Analysis

1st Edition
Volume 189
September 20, 2001
K.D. Bierstedt + 3 more
English
eBook
9 7 8 0 0 8 0 5 1 5 9 2 2

This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.

General Theory of C*-Algebras

1st Edition
Volume 3
July 11, 2001
Corneliu Constantinescu
English
eBook
9 7 8 0 0 8 0 5 2 8 3 4 2

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