書目名稱 | Limit Operators and Their Applications in Operator Theory | 編輯 | Vladimir Rabinovich,Bernd Silbermann,Steffen Roch | 視頻video | http://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 |  | 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 | 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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