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AuthorBerezansky, Yurij M. author
TitleFunctional Analysis [electronic resource] : Vol.II / by Yurij M. Berezansky, Zinovij G. Sheftel, Georgij F. Us
ImprintBasel : Birkhรคuser Basel, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9024-3
Descript 293 p. online resource

SUMMARY

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


CONTENT

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 -- 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 Cร rleman Operators -- 16 Differential Operators -- 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 Greenโ{128}{153}s Function of Elliptic Differential Operators -- 6 Ordinary Differential Operators -- Bibliographical Notes -- References


Mathematics Mathematical analysis Analysis (Mathematics) Functional analysis Mathematics Functional Analysis Analysis



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