Operator Theory and Ill-Posed Problems
Seiten
| Ausstattung: eBook & Hardcover
2011
De Gruyter
9783111828251 (ISBN)
De Gruyter
9783111828251 (ISBN)
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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
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.
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.
Mikhail M. Lavrent'ev †; Lev Ja. Savel'ev, Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia.
| Reihe/Serie | Inverse and Ill-Posed Problems Series ; 50 |
|---|---|
| Zusatzinfo | Includes a print version and an ebook |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Gewicht | 1001 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Schlagworte | abstract algebra • Functional Analysis • Function Operator Classes • function spaces • Funktionalanalysis • ill-posed problems • Inverses Problem • linear algebra • Linear Operators • Multilinear Algebra • Nonlinear Operators • operators • Operatortheorie • operator theory • Operator Theory; Ill-posed Problems; Functional Analysis; Abstract Algebra; Linear Algebra; Multilinear Algebra; Operators; Function Spaces; Function Operator Classes; Linear Operators; Nonlinear Operators |
| ISBN-13 | 9783111828251 / 9783111828251 |
| Zustand | Neuware |
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