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Operator theory : nonclassical problems

Author: S G Pyatkov
Publisher: Utrecht ; Boston : VSP, 2002.
Series: Inverse and ill-posed problems series.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Pyatkov, S.G.
Operator theory
(DLC) 2002512416
(OCoLC)51216246
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: S G Pyatkov
ISBN: 9783110900163 3110900165
OCLC Number: 859155009
Description: 1 online resource (ix, 346 pages).
Contents: ""Chapter 1. Indefinite inner product spaces. Linear operators. Interpolation""; ""1. Indefinite inner product spaces""; ""1.1. Definitions""; ""1.2. Krein spaces""; ""1.3. The Gram operator. W-spaces""; ""1.4. J-orthogonal complements. Projective completeness""; ""1.5. J-orthonormalized systems""; ""2. The basic classes of operators in Krein spaces""; ""2.1. J-dissipative operators""; ""2.2. J-selfadjoint operators""; ""3. Interpolation of Banach and Hilbert spaces and applications""; ""3.1. Preliminaries""; ""3.2. Continuity of some functional in a Hilbert scale"" ""3.3. Separation of the spectrum of an unbounded operator""""3.4. Interpolation properties of bases""; ""4. The existence of maximal semidefinite invariant subspaces for J-dissipative operators""; ""5. First order equations. Decomposition of a solution""; ""5.1. Function spaces""; ""5.2. The Cauchy problem""; ""5.3. Auxiliary definitions. Some properties of imaginary powers of operators""; ""5.4. Solvability of the Cauchy problem in the original Banach space""; ""5.5. Adjoint problems""; ""5.6. Arbitrary operators. Phase spaces""; ""5.7. Remarks and examples"" ""Chapter 2. Spectral theory for linear selfadjoint pencils""""1. Examples""; ""1.1. Selfadjoint pencils""; ""1.2. Elliptic eigenvalue problems with indefinite weight function""; ""2. Basic assumptions. The structure of root subspaces""; ""3. The Riesz basis property. Invariant subspaces""; ""3.1. Basis property""; ""3.2. Invariant subspaces. Some applications""; ""4. Sufficient conditions""; ""Chapter 3. Elliptic eigenvalue problems with an indefinite weight function""; ""1. Auxiliary function spaces. Interpolation""; ""1.1. Definitions""; ""1.2. Interpolation of weighted Sobolev spaces"" ""1.3. Inequalities of the Hardy type""""2. Preliminaries. Basic assumptions""; ""2.1. Variational statement""; ""2.2. Elliptic problems""; ""3. Basisness theorems""; ""3.1. The general case""; ""3.2. The one-dimensional case""; ""4. Examples and counterexamples""; ""Chapter 4. Operator-differential equations""; ""1. Generalized solutions. Positive definite case""; ""1.1. Preliminaries""; ""1.2. Uniqueness and existence theorems""; ""2. Degenerate case""; ""2.1. Preliminaries""; ""2.2. Solvability theorems. The case of a bounded interval"" ""2.3. Solvability theorems. The case of the interval (0, 8)""""2.4. Smoothness of solutions. Orthogonality conditions""; ""2.5. The periodic problem. Linear inverse problems""; ""3. The Fourier method""; ""3.1. Representation of solutions. First order equations""; ""3.2. Some problems for the second order equations""; ""4. Some applications to partial differential equations""; ""4.1. Higher order parabolic equations with changing time direction""; ""4.2. Second order parabolic equations with changing time direction""; ""4.3. Orthogonality conditions. Parabolic equations""
Series Title: Inverse and ill-posed problems series.
Responsibility: S.G. Pyatkov.

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