The Resource Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource)

Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource)

Label
Complete Second Order Linear Differential Equations in Hilbert Spaces
Title
Complete Second Order Linear Differential Equations in Hilbert Spaces
Statement of responsibility
by Alexander Ya. Shklyar
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood
Member of
Is Subseries of
http://library.link/vocab/creatorName
Shklyar, Alexander Ya
Dewey number
515.7
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
ZDZVw0jvPgI
Image bit depth
0
Language note
English
LC call number
QA319-329.9
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Operator Theory: Advances and Applications,
Series volume
92
http://library.link/vocab/subjectName
  • Functional analysis
  • Global analysis (Mathematics)
  • Functional Analysis
  • Analysis
Label
Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I. Well-posedness of boundary-value problems -- to Part I -- 1. Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of well-posedness of boundary-value problems -- 2. Well-posedness of boundary-value problems for equation (1) in the case of commuting self-adjoint A and B -- 3. The Cauchy problem -- 4. Boundary-value problems on a finite segment -- II. Initial data of solutions -- to Part II -- 5. Boundary behaviour of an integral transform R(t) as t ? 0 depending on the sub-integral measure -- 6. Initial data of solutions -- III. Extension, stability, and stabilization of weak solutions -- to Part III -- 7. The general form of weak solutions -- 8. Fatou-Riesz property -- 9. Extension of weak solutions -- 10. Stability and stabilization of weak solutions -- IV. Boundary-value problems on a half-line -- to Part IV -- 11. The Dirichlet problem on a half-line -- 12. The Neumann problem on a half-line -- Commentaries on the literature -- List of symbols
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XII, 220 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034891875
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-0348-9187-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101847
  • (SSID)ssj0001296181
  • (PQKBManifestationID)11857671
  • (PQKBTitleCode)TC0001296181
  • (PQKBWorkID)11347788
  • (PQKB)10055893
  • (DE-He213)978-3-0348-9187-5
  • (MiAaPQ)EBC3088591
  • (EXLCZ)993400000000101847
Label
Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I. Well-posedness of boundary-value problems -- to Part I -- 1. Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of well-posedness of boundary-value problems -- 2. Well-posedness of boundary-value problems for equation (1) in the case of commuting self-adjoint A and B -- 3. The Cauchy problem -- 4. Boundary-value problems on a finite segment -- II. Initial data of solutions -- to Part II -- 5. Boundary behaviour of an integral transform R(t) as t ? 0 depending on the sub-integral measure -- 6. Initial data of solutions -- III. Extension, stability, and stabilization of weak solutions -- to Part III -- 7. The general form of weak solutions -- 8. Fatou-Riesz property -- 9. Extension of weak solutions -- 10. Stability and stabilization of weak solutions -- IV. Boundary-value problems on a half-line -- to Part IV -- 11. The Dirichlet problem on a half-line -- 12. The Neumann problem on a half-line -- Commentaries on the literature -- List of symbols
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XII, 220 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034891875
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-0348-9187-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101847
  • (SSID)ssj0001296181
  • (PQKBManifestationID)11857671
  • (PQKBTitleCode)TC0001296181
  • (PQKBWorkID)11347788
  • (PQKB)10055893
  • (DE-He213)978-3-0348-9187-5
  • (MiAaPQ)EBC3088591
  • (EXLCZ)993400000000101847

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