Operator theory and ill-posed problems / M.M. Lavrent'ev and L.Ya. Savel'ev.

Format:

Book

Author/Creator:

Lavrentev, M. M. (Mikhail Mikhailovich)

Contributor:

Savelev, L. IA. (Lev IAkovlevich)

Series:

Inverse and III-Posed Problems

Inverse and Ill-Posed Problems Series ; 50

Language:

English

Subjects (All):

Operator theory--Textbooks.

Operator theory.

Numerical analysis--Improperly posed problems--Textbooks.

Numerical analysis.

Physical Description:

1 online resource (696 p.)

Place of Publication:

Leiden ; Boston : VSP, 2006.

Language Note:

English

Summary:

This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.

Contents:

Frontmatter

Contents

Preface

BASIC CONCEPTS

Chapter 1. Set theory

Chapter 2. Algebra

Chapter 3. Calculus

OPERATORS

Chapter 4. Linear operators

Chapter 5. Nonlinear operators

ILL-POSED PROBLEMS

Chapter 6. Classic problems

Chapter 7. Ill-posed problems

Chapter 8. Physical problems leading to ill-posed problems

Chapter 9. Operator and integral equations

Chapter 10. Evolution equations

Chapter 11. Problems of integral geometry

Chapter 12. Inverse problems

Chapter 13. Several areas of the theory of ill-posed problems, inverse problems, and applications

Bibliography

Index

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Includes bibliographical references (p. [662]-672) and index.

ISBN:

9783110960723

3110960729

OCLC:

840446279