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＜電子ブック＞
Linear Integral Equations / by Rainer Kress
(Applied Mathematical Sciences. ISSN:2196968X ; 82)

版	3rd ed. 2014.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XVI, 412 p. 1 illus : online resource
著者標目	*Kress, Rainer author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Numerical analysis LCSH:Measure theory LCSH:Signal processing FREE:Analysis FREE:Numerical Analysis FREE:Measure and Integration FREE:Signal, Speech and Image Processing
一般注記	Normed Spaces -- Bounded and Compact Operators -- Riesz Theory -- Dual Systems and Fredholm Alternative -- Regularization in Dual Systems -- Potential Theory -- Singular Integral Equations -- Sobolev Spaces -- The Heat Equation -- Operator Approximations .-Degenerate Kernel Approximation -- Quadrature Methods -- Projection Methods -- Iterative Solution and Stability -- Equations of the First Kind -- Tikhonov Regularization -- Regularization by Discretization -- Inverse Boundary Value Problems -- References -- Index This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter.     For this third edition in  order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text.The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods   Reviews of earlier editions:   "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000)   "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modernframework without being too abstract."  (ZbMath, 1999)   HTTP:URL=https://doi.org/10.1007/978-1-4614-9593-2

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