| 书目名称 | Limit Operators and Their Applications in Operator Theory | | 编辑 | Vladimir Rabinovich,Bernd Silbermann,Steffen Roch | | 视频video | | | 概述 | First monograph devoted to the limit operators method, including the study of general band-dominated operators and their Fredholm theory | | 丛书名称 | Operator Theory: Advances and Applications | | 图书封面 |  | | 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 | | 关键词 | Operator theory; Singular integral; convolution; limit operators; pseudodifferential operators | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-7911-8 | | isbn_softcover | 978-3-0348-9619-1 | | isbn_ebook | 978-3-0348-7911-8Series ISSN 0255-0156 Series E-ISSN 2296-4878 | | issn_series | 0255-0156 | | copyright | Springer Basel AG 2004 |
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发表于 2025-3-21 18:31:03
