Operator Theory and Ill-Posed Problems / / Lev Ja. Savel'ev, Mikhail M. Lavrent'ev.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Lavrent'ev, Mikhail M.,; Savel'ev, Lev Ja.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2006
• Year of Publication: 2011
• Language: English
• Series: Inverse and Ill-Posed Problems Series , 50
• Physical Description: 1 online resource (680 p.)

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.

Table of Contents

i-iv -- 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