Operator Theory and Ill-Posed Problems

Operator Theory and Ill-Posed Problems

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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 qBasic Conceptsq 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 qOperatorsq 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 qIll-Posed Problemsq 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.... makes this orientation negative. The sign of the integral changes accordingly: / w = / we 0 Ac)alt;-1)) - (10 101(8) ds = a€” /it ... a horizontal cylinder in R3 = R X R2 whose projection onto a vertical plane is the circle S(0, 1a#39;). Using the rule for theanbsp;...

Title:Operator Theory and Ill-Posed Problems
Author:Mikhail M. Lavrent'ev, Lev Ja. Savel'ev
Publisher:Walter de Gruyter - 2006-01-01


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