Spectral theory of linear differential operators and comparison algebras /

The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cordes, H. O. (Heinz Otto), 1925-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, ©1987.
Colección:London Mathematical Society lecture note series ; 76.
Temas:
Differential operators.
Linear operators.
Opérateurs différentiels.
Opérateurs linéaires.
MATHEMATICS > Functional Analysis.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title
  • Copyright
  • Preface
  • Contents
  • Chapter 1. Abstract spectral theory in Hilbert spaces
  • 1.1. Unbounded linear operators on Banach and Hilbert spaces
  • 1.2. Self-adjoint extensions of hermitian operators
  • 1.3. On the spectral theorem for self-adjoint operators.
  • 1.4. Proof of the spectral theorem
  • 1.5. A result on powers of positive operators
  • 1.6. On HS-chains 2
  • Chapter 2. Spectral theory of differential operators
  • 2.1. Linear differential operators on a subdomain of ln
  • 2.2. Generalized boundary problems.
  • Ordinary differential expressions
  • 2.3. Singular endpoints of a 2r-th order Sturm-Liouville problem
  • 2.4. The spectral theorem for a second order expression
  • Chapter 3. Second order elliptic expressions on manifolds
  • 3.1. 2-nd order partial differential expressions on manifolds
  • Weyl!s lemma
  • Dirichlet operator
  • 3.2. Boundary regularity for the Dirichlet realization
  • 3.3. Compactness of the resolvent of the Friedrichs extension
  • 3.4. A Green's function for H and Hd and a mean value inequality
  • 3.5. Harnack inequality
  • Dirichlet problem.
  • Maximum principle
  • 3.6. Change of dependent variable
  • normal forms
  • positivity of the Green's function
  • Chapter 4. Essential self-adjointness of the Minimal Operator
  • 4.1. Essential self-adjointness of powers of H0
  • 4.2. Essential self-adjointness of HQ
  • 4.3. Proof of theorem 1.1
  • 4.4. Proof of Frehse's theorem
  • 4.5. More criteria for essential self-adjointness
  • Chapter 5. C -Comparison algebras
  • 5.1. Comparison operators and comparison algebras
  • 5.2. Differential expressions of order _<2.
  • 5.3. Compactness criteria for commutators
  • 5.4. Comparison algebras with compact commutators
  • 5.5. A discussion of one-dimensional problems
  • 5.6. An expansion for expressions within reach of an algebra C
  • Chapter 6. Minimal comparison algebra and wave front space.
  • 6.1. The local invariance of the minimal comparison algebra
  • 6.2. The wave front space
  • 6.3. Differential expressions within reach of the algebra J0
  • 6.4. The Sobolev estimate for elliptic expressions expressions on a compact
  • Chapter 7. The secondary symbol space.
  • 7.1. The symbol space of a general comparison algebra
  • 7.2. The space flAw, and some examples
  • 7.3. Stronger conditions and more detail on M\W .
  • 7.4. More structure of ffi, and more on examples
  • Chapter 8. Comparison algebras with non-compact commutators
  • 8.1. An algebra invariant under a discrete translation group
  • 8.2. A C -algebra on a poly-cylinder
  • 8.3. Algebra surgery
  • 8.4. Complete Riemannian manifolds with cylindrical ends
  • Chapter 9. H -Algebras
  • higher order s operators within reach.

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