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Titlebook: Limit Operators and Their Applications in Operator Theory; Vladimir Rabinovich,Bernd Silbermann,Steffen Roch Book 2004 Springer Basel AG 2

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發(fā)表于 2025-3-21 18:31:03 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Limit Operators and Their Applications in Operator Theory
編輯Vladimir Rabinovich,Bernd Silbermann,Steffen Roch
視頻videohttp://file.papertrans.cn/587/586156/586156.mp4
概述First monograph devoted to the limit operators method, including the study of general band-dominated operators and their Fredholm theory
叢書名稱Operator Theory: Advances and Applications
圖書封面Titlebook: Limit Operators and Their Applications in Operator Theory;  Vladimir Rabinovich,Bernd Silbermann,Steffen Roch Book 2004 Springer Basel AG 2
描述This text has two goals. It describes a topic: band and band-dominated operators and their Fredholm theory, and it introduces a method to study this topic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of [2(Z) is the family of sequences (ei)iEZ where ei = (. . . ,0,0, 1,0,0, . . . ) with the 1 standing at the ith place. Every bounded linear operator A on H can be described by a two-sided infinite matrix (aij)i,jEZ with respect to this basis, where aij = (Aej, ei)‘ The band operators on H are just the operators with a matrix representation of finite band-width, i. e. , the operators for which aij = 0 whenever Ii - jl > k for some k. Operators which are in the norm closure ofthe algebra of all band operators are called band-dominated. Needless to say that band and band- dominated operators appear in numerous branches of mathematics. Archetypal examples come from discretizations of partial differential operators. It is easy to check that ever
出版日期Book 2004
關(guān)鍵詞Operator theory; Singular integral; convolution; limit operators; pseudodifferential operators
版次1
doihttps://doi.org/10.1007/978-3-0348-7911-8
isbn_softcover978-3-0348-9619-1
isbn_ebook978-3-0348-7911-8Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightSpringer Basel AG 2004
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Book 2004opic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of
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Fredholmness of Band-dominated Operators,e, then the operator is .-Fredholm. The class under consideration consists of band and band-dominated operators which act on .-spaces over ?.. In the forthcoming chapters we will point out that this class is large enough to include, e.g., discretizations of convolution operators and of pseudodiffere
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,Convolution Type Operators on ?,, 1).) after a suitable discretization and which are, thus, subject to the general theory developed in the previous chapter. Prominent members of this class are the Fourier convolution operators, certain pseudodifferential operators as well as operators in finite differences. We employ the close rel
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Pseudodifference Operators,e analogs of the standard pseudodifferential operators on?. (see, for instance, the monographs [175, 164, 174, 76]). Notice also that, under some special conditions on the symbol a, the dual operator to a pseudodifference operator with respect to the discrete Fourier transform is a pseudodifferentia
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