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140122 ||| eng |
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|a 9783034890243
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| 100 |
1 |
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|a Berezansky, Yurij M.
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| 245 |
0 |
0 |
|a Functional Analysis
|h Elektronische Ressource
|b Vol.II
|c by Yurij M. Berezansky, Zinovij G. Sheftel, Georgij F. Us
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| 250 |
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|a 1st ed. 1996
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| 260 |
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|a Basel
|b Birkhäuser
|c 1996, 1996
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| 300 |
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|a 293 p
|b online resource
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| 505 |
0 |
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|a 7 Spectral of Representation One-Parameter Unitary Groups and Operator Differential Equations -- 8 Evolutionary Criteria of Selfadjointness -- 9 Quasianalytic Criteria of Selfadjointness and Commutability -- 10 Selfadjointness of Perturbed Operators -- 14 Rigged Spaces -- 1 Hilbert Riggings -- 2 Rigging of Hilbert Spaces by Linear Topological Spaces -- 3 Sobolev Spaces in Bounded Domains -- 4 Sobolev Spaces in Unbounded Domains. Classical Spaces of Test Functions -- 5 Tensor Products of Spaces -- 6 The Kernel Theorem -- 7 Completions of a Space with Respect to Two Different Norms -- 8 Semibounded Bilinear Forms -- 15 Expansion in Generalized Eigenvectors -- 1 Differentiation of Operator-Valued Measures and Resolutions of the Identity -- 2 Generalized Eigenvectors and the Projection Spectral Theorem -- 3 Fourier Transformation in Generalized Eigenvectors and the Direct Integral of Hilbert Spaces -- 4 Expansion in Eigenfunctions of Càrleman Operators -- 16 Differential Operators --
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| 505 |
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|a 12 General Theory of Unbounded Operators in Hilbert Spaces -- 1 Definition of an Unbounded Operator. The Graph of an Operator -- 2 Closed and Closable Operators. Differential Operators -- 3 The Adjoint Operator -- 4 Defect Numbers of General Operators -- 5 Hermitian and Selfadjoint Operators. General Theory -- 6 Isometric and Unitary Operators. Cayley Transformation -- 7 Extensions of Hermitian Operators to Selfadjoint Operators -- 13 Spectral Decompositions of Selfadjoint, Unitary, and Normal Operators. Criteria of Selfadjointness -- 1 The Resolution of the Identity and Its Properties -- 2 The Construction of Spectral Integrals -- 3 Image of a Resolution of the Identity. Change of Variables in Spectral Integrals. Product of Resolutions of the Identity -- 4 Spectral Decomposition of Bounded Selfadjoint Operators -- 5 Spectral Decompositions for Unitary and Bounded Normal Operators -- 6 Spectral Decompositions of Unbounded Operators --
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| 505 |
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|a 1 Theorem on Isomorphisms for Elliptic Operators -- 2 Local Smoothing of Generalized Solutions of Elliptic Equations -- 3 Elliptic Differential Operators in a Domain with Boundary -- 4 Differential Operators in ?N -- 5 Expansion in Eigenfunctions and Green’s Function of Elliptic Differential Operators -- 6 Ordinary Differential Operators -- Bibliographical Notes -- References
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| 653 |
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|a Functional analysis
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Analysis
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| 700 |
1 |
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|a Sheftel, Zinovij G.
|e [author]
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| 700 |
1 |
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|a Us, Georgij F.
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a Operator Theory: Advances and Applications
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| 028 |
5 |
0 |
|a 10.1007/978-3-0348-9024-3
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-0348-9024-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515.7
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| 520 |
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|a Functional Analysis is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathemati- cal physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more ad- vanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual
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