Operator theory : nonclassical problems /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pyatkov, S. G.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht ; Boston : VSP, 2002.
Colección:Inverse and ill-posed problems series.
Temas:
Operator theory.
Interpolation spaces.
Nonclassical mathematical logic.
Banach spaces.
Théorie des opérateurs.
Espaces d'interpolation.
Logique mathématique non classique.
Espaces de Banach.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Banach spaces
Interpolation spaces
Nonclassical mathematical logic
Operator theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 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
  • 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
  • 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
  • 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

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