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Unbounded Self-adjoint Operators on Hilbert Space / by Konrad Schmüdgen
(Graduate Texts in Mathematics. ISSN:21975612 ; 265)
版 | 1st ed. 2012. |
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出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
出版年 | 2012 |
本文言語 | 英語 |
大きさ | XX, 432 p : online resource |
著者標目 | *Schmüdgen, Konrad author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Mathematical physics LCSH:Operator theory FREE:Functional Analysis FREE:Mathematical Methods in Physics FREE:Operator Theory FREE:Mathematical Physics FREE:Theoretical, Mathematical and Computational Physics |
一般注記 | I Basics onClosed Operators -- 1 Closed Operators and Adjoint Operators -- 2 Spectrum of Closed Operators -- 3 Some Classes of Unbounded Operators -- II Spectral Theory -- 4 Spectral Measures and Spectral Integrals -- 5 Spectral Decomposition of Selfadjoint and Normal Operators -- III Special Topics -- 6 One-Parameter Groups and Semigroups of Operators -- 7 Miscellaneous -- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators -- 8 Perturbations of Selfadjoint Operators -- 9 Trace Class Perturbations of Spectra of Selfadjoint Operators -- V Forms and Operators -- 10 Semibounded Forms and Selfadjoint Operators -- 11 Sectorial Forms and m-Sectorial Operators -- 12 Discrete Spectrum of Selfadjoint Operators -- VI Selfadjoint Extention Theory of Symmetric Operators -- 13 Selfajoint Extensions: Cayley Transform and Krein Transform -- 14 Selfadjoint Extensions: Boundary Triplets -- 15 Sturm-Liouville Operators -- One-Dimensional Moment Problem The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension HTTP:URL=https://doi.org/10.1007/978-94-007-4753-1 |
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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 | 9789400747531 |
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EB00234635 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000118414 |
ISBN | 9789400747531 |
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