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Titlebook: Spectral Theory of Approximation Methods for Convolution Equations; Roland Hagen,Steffen Roch,Bernd Silbermann Book 1995 Birkhäuser Verlag

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发表于 2025-3-21 19:08:52 | 显示全部楼层 |阅读模式
书目名称Spectral Theory of Approximation Methods for Convolution Equations
编辑Roland Hagen,Steffen Roch,Bernd Silbermann
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Spectral Theory of Approximation Methods for Convolution Equations;  Roland Hagen,Steffen Roch,Bernd Silbermann Book 1995 Birkhäuser Verlag
描述The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.
出版日期Book 1995
关键词Banach algebra; C*-algebra; Operator theory; Singular integral; convolution
版次1
doihttps://doi.org/10.1007/978-3-0348-9067-0
isbn_softcover978-3-0348-9891-1
isbn_ebook978-3-0348-9067-0Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightBirkhäuser Verlag 1995
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发表于 2025-3-21 21:59:39 | 显示全部楼层
Manifolds, Similarly, an approximation sequence over a smooth curve behaves locally as a certain sequence over the tangent, i.e. over the real axis, and these are just the sequences we dealt with in the third chapter.
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Invertibility in Banach algebras,ows to tackle a lot of different invertibility problems (including the Fredholmness of Toeplitz and Wiener-Hopf operators and the stability of spline approximation methods for singular integral and Mellin operators) from a common point of view.
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Around finite sections of integral operators, solve instead of (1) equations of the form . where the projections . are given by.and where . is positive (and large). The . is said to apply to equation (1) if the equations (2) are uniquely solvable for all right sides . and for all . large enough (say, .), and if their solutions . converge to a solution .of (1) as . in the norm of ..
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Invertibility in Banach algebras,theories in Banach algebras. Then to give the reader a first idea of the usefulness of abstract local principles, we examine the so-called finite section method for Toeplitz operators. From this application we are finally going to extract a general scheme of using Banach algebra techniques which all
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Singularities, in the preceding sections: viz. the analytic singularities caused by discontinuous coefficients in the operators. These singularities bring forth undetermined compact perturbations in stability conditions (compare the operators .. in Theorems 3.9 and 3.11) or, at worst, perturbations behaving irreg
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