| Description |
1 online resource (ix, 346 pages) |
| Series |
Inverse and ill-posed problems series, 1381-4524 |
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Inverse and ill-posed problems series. 1381-4524
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| 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 |
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3.3. Separation of the spectrum of an unbounded operator3.4. 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 |
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Chapter 2. Spectral theory for linear selfadjoint pencils1. 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 |
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1.3. Inequalities of the Hardy type2. 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 |
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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 |
| Bibliography |
Includes bibliographical references (pages 323-346) and index |
| Notes |
Print version record |
| Subject |
Operator theory.
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Interpolation spaces.
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Nonclassical mathematical logic.
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Banach spaces.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Banach spaces
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Interpolation spaces
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Nonclassical mathematical logic
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Operator theory
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| Form |
Electronic book
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| ISBN |
9783110900163 |
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3110900165 |
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