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The Functional Calculus for Sectorial Operators / by Markus Haase
(Operator Theory: Advances and Applications. ISSN:22964878 ; 169)
版 | 1st ed. 2006. |
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出版者 | Basel : Birkhäuser Basel : Imprint: Birkhäuser |
出版年 | 2006 |
本文言語 | 英語 |
大きさ | XIV, 394 p. 8 illus : online resource |
著者標目 | *Haase, Markus author SpringerLink (Online service) |
件 名 | LCSH:Operator theory LCSH:Functional analysis FREE:Operator Theory FREE:Functional Analysis |
一般注記 | Axiomatics for Functional Calculi -- The Functional Calculus for Sectorial Operators -- Fractional Powers and Semigroups -- Strip-type Operators and the Logarithm -- The Boundedness of the H?-Calculus -- Interpolation Spaces -- The Functional Calculus on Hilbert Spaces -- Differential Operators -- Mixed Topics The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolic type. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large class of (even meromorphic) functions. With this functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with the theory of interpolation spaces. A chapter is devoted to the exciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example to elliptic operators, to numerical approximations of parabolic equations, and to the maximal regularity problem. This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolution equations, and harmonic analysis. It is an original and comprehensive exposition of the theory as a whole. Written in a clear style and optimally organised, it will prove useful for the advanced graduate as well as for the experienced researcher HTTP:URL=https://doi.org/10.1007/3-7643-7698-8 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783764376987 |
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EB00238804 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA329-329.9 DC23:515,724 |
書誌ID | 4000116642 |
ISBN | 9783764376987 |
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※2017年9月4日以降