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E-book
Author Cordes, H. O. (Heinz Otto), 1925-

Title Spectral theory of linear differential operators and comparison algebras / Heinz Otto Cordes
Published Cambridge ; New York : Cambridge University Press, ©1987

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Description 1 online resource (356 pages)
Series London Mathematical Society lecture note series ; 76
London Mathematical Society lecture note series ; 76.
Contents 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
Summary 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
Bibliography Includes bibliographical references and index
Notes English
Print version record
Subject Differential operators.
Linear operators.
MATHEMATICS -- Functional Analysis.
Differential operators
Linear operators
Form Electronic book
ISBN 9781107361102
1107361109
9780511662836
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