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Overview
In this easily-accessible textbook, the authors integrate the ill-posed problem theory and its underlying mathematical apparatus. This comprehensive work includes descriptions of recent results and a presentation of actual applications of the ill-posed problem theory. The first part of the book describes the differentiation of normed space mappings, the integration of the functions of abstract variables, and the theory of linear operators. The second section deals with the mathematical physics connected to integral equations of the first type, and with the bases of operator equation theory.
Synopsis
In this easily-accessible textbook, the authors integrate the ill-posed problem theory and its underlying mathematical apparatus. This comprehensive work includes descriptions of recent results and a presentation of actual applications of the ill-posed problem theory. The first part of the book describes the differentiation of normed space mappings, the integration of the functions of abstract variables, and the theory of linear operators. The second section deals with the mathematical physics connected to integral equations of the first type, and with the bases of operator equation theory.
Booknews
The section on linear operators covers differential calculus in normed spaces, linear mappings, integration of functions of an abstract variable, and elements of the theory of linear operators in normed spaces, with ample treatment of spectral theory of operators. The main content of the book consists of five chapters devoted to ill- posed problem theory and its applications, describing some classical ill-posed problems reducing Fredholm's equations, ill-conditioned problems in mathematical physics, operator and integral equations, and problems of integral geometry. This revised English edition contains two short chapters on tomographic applications, logarithmic convexity, and inversion formulas for integral equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)