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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)
Resource Information
The item Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 wellposedness 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 selfcontained 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
 Language

 eng
 eng
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XII, 220 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 I. Wellposedness of boundaryvalue problems
 to Part I
 1. Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of wellposedness of boundaryvalue problems
 2. Wellposedness of boundaryvalue problems for equation (1) in the case of commuting selfadjoint A and B
 3. The Cauchy problem
 4. Boundaryvalue 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 subintegral 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. FatouRiesz property
 9. Extension of weak solutions
 10. Stability and stabilization of weak solutions
 IV. Boundaryvalue problems on a halfline
 to Part IV
 11. The Dirichlet problem on a halfline
 12. The Neumann problem on a halfline
 Commentaries on the literature
 List of symbols
 Isbn
 9783034891875
 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
 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 wellposedness 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 selfcontained 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
 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
 QA319329.9
 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)
 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. Wellposedness of boundaryvalue problems  to Part I  1. Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of wellposedness of boundaryvalue problems  2. Wellposedness of boundaryvalue problems for equation (1) in the case of commuting selfadjoint A and B  3. The Cauchy problem  4. Boundaryvalue 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 subintegral 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. FatouRiesz property  9. Extension of weak solutions  10. Stability and stabilization of weak solutions  IV. Boundaryvalue problems on a halfline  to Part IV  11. The Dirichlet problem on a halfline  12. The Neumann problem on a halfline  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
 10.1007/9783034891875
 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
 (DEHe213)9783034891875
 (MiAaPQ)EBC3088591
 (EXLCZ)993400000000101847
 Label
 Complete Second Order Linear Differential Equations in Hilbert Spaces, by Alexander Ya. Shklyar, (electronic resource)
 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. Wellposedness of boundaryvalue problems  to Part I  1. Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of wellposedness of boundaryvalue problems  2. Wellposedness of boundaryvalue problems for equation (1) in the case of commuting selfadjoint A and B  3. The Cauchy problem  4. Boundaryvalue 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 subintegral 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. FatouRiesz property  9. Extension of weak solutions  10. Stability and stabilization of weak solutions  IV. Boundaryvalue problems on a halfline  to Part IV  11. The Dirichlet problem on a halfline  12. The Neumann problem on a halfline  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
 10.1007/9783034891875
 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
 (DEHe213)9783034891875
 (MiAaPQ)EBC3088591
 (EXLCZ)993400000000101847
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