The Resource Spectral theory of linear differential operators and comparison algebras, H.O. Cordes, (electronic resource)

Spectral theory of linear differential operators and comparison algebras, H.O. Cordes, (electronic resource)

Label
Spectral theory of linear differential operators and comparison algebras
Title
Spectral theory of linear differential operators and comparison algebras
Statement of responsibility
H.O. Cordes
Creator
Subject
Genre
Language
  • eng
  • eng
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
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1925-
http://library.link/vocab/creatorName
Cordes, H. O.
Dewey number
  • 515.7/242
  • 515.7242
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA329.4
LC item number
.C67 1987
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
London Mathematical Society lecture note series,
Series volume
76
http://library.link/vocab/subjectName
  • Differential operators
  • Linear operators
Label
Spectral theory of linear differential operators and comparison algebras, H.O. Cordes, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographic references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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 problem2.4. 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 functionChapter 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 CChapter 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 commutators8.1. 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; 9.1. Higher order Sobolev spaces and H -comparison algebras; 9.2. Closer analysis of some of the conditions (1.) and (m.); 9.3. Higher order differential expressions within reach of C or Cs; 9.4. Symbol calculus in W; 9.5. Local properties of the Sobolev spaces Hs
  • 9.6. Sobolev norms of integral order
Dimensions
unknown
Extent
1 online resource (354 p.)
Form of item
online
Isbn
9781107361102
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2610000000003328
  • (EBL)1182399
  • (SSID)ssj0000464181
  • (PQKBManifestationID)11322841
  • (PQKBTitleCode)TC0000464181
  • (PQKBWorkID)10420718
  • (PQKB)10486144
  • (UkCbUP)CR9780511662836
  • (MiAaPQ)EBC1182399
  • (EXLCZ)992610000000003328
Label
Spectral theory of linear differential operators and comparison algebras, H.O. Cordes, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographic references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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 problem2.4. 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 functionChapter 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 CChapter 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 commutators8.1. 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; 9.1. Higher order Sobolev spaces and H -comparison algebras; 9.2. Closer analysis of some of the conditions (1.) and (m.); 9.3. Higher order differential expressions within reach of C or Cs; 9.4. Symbol calculus in W; 9.5. Local properties of the Sobolev spaces Hs
  • 9.6. Sobolev norms of integral order
Dimensions
unknown
Extent
1 online resource (354 p.)
Form of item
online
Isbn
9781107361102
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2610000000003328
  • (EBL)1182399
  • (SSID)ssj0000464181
  • (PQKBManifestationID)11322841
  • (PQKBTitleCode)TC0000464181
  • (PQKBWorkID)10420718
  • (PQKB)10486144
  • (UkCbUP)CR9780511662836
  • (MiAaPQ)EBC1182399
  • (EXLCZ)992610000000003328

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