The Resource The method of rigged spaces in singular perturbation theory of self-adjoint operators, Volodymyr Koshmanenko, Mykola Dudkin

The method of rigged spaces in singular perturbation theory of self-adjoint operators, Volodymyr Koshmanenko, Mykola Dudkin

Label
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Title
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Statement of responsibility
Volodymyr Koshmanenko, Mykola Dudkin
Creator
Contributor
Author
Translator
Subject
Language
  • eng
  • ukr
  • eng
Summary
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac e-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.--
Member of
Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorName
Koshmanenko, V. D
Illustrations
illustrations
Index
index present
LC call number
QA372
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Dudkin, Mykola
  • Koshmanenko, Nataliia
Series statement
Operator theory: Advances and applications,
Series volume
volume 253
http://library.link/vocab/subjectName
  • Singular perturbations (Mathematics)
  • Hilbert space
  • Operator theory
Label
The method of rigged spaces in singular perturbation theory of self-adjoint operators, Volodymyr Koshmanenko, Mykola Dudkin
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-29535-0
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Introduction -- 1. Preliminaries -- 2. Symmetric Operators and Closable Quadratic Forms -- 3. Self-adjoint Extensions of Symmetric Operators -- 4. Rigged Hilbert Spaces -- 5. Singular Quadratic Forms -- 6. Dense Subspaces in Scales of Hilbert Spaces -- 7. Singular Perturbations of Self-adjoint Operators -- 8. Super-singular Perturbations -- 9. Some Aspects of the Spectral Theory -- References -- Subject Index -- Notation Index
Dimensions
unknown
Extent
1 online resource (xx, 237 pages)
File format
unknown
Form of item
online
Isbn
9783319295350
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-29535-0
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)953455878
  • (OCoLC)ocn953455878
Label
The method of rigged spaces in singular perturbation theory of self-adjoint operators, Volodymyr Koshmanenko, Mykola Dudkin
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-29535-0
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Introduction -- 1. Preliminaries -- 2. Symmetric Operators and Closable Quadratic Forms -- 3. Self-adjoint Extensions of Symmetric Operators -- 4. Rigged Hilbert Spaces -- 5. Singular Quadratic Forms -- 6. Dense Subspaces in Scales of Hilbert Spaces -- 7. Singular Perturbations of Self-adjoint Operators -- 8. Super-singular Perturbations -- 9. Some Aspects of the Spectral Theory -- References -- Subject Index -- Notation Index
Dimensions
unknown
Extent
1 online resource (xx, 237 pages)
File format
unknown
Form of item
online
Isbn
9783319295350
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-29535-0
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)953455878
  • (OCoLC)ocn953455878

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