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The Resource The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, by Volodymyr Koshmanenko, Mykola Dudkin, (electronic resource)

The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, by Volodymyr Koshmanenko, Mykola Dudkin, (electronic resource)

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
by Volodymyr Koshmanenko, Mykola Dudkin
Creator
Contributor
Author
Subject
Language
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
http://library.link/vocab/creatorName
Koshmanenko, Volodymyr
Dewey number
223
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Dudkin, Mykola.
Series statement
  • Springer eBooks
  • Operator Theory: Advances and Applications,
Series volume
253
http://library.link/vocab/subjectName
  • Mathematics
  • Measure theory
  • Operator theory
  • Mathematical physics
Label
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, by Volodymyr Koshmanenko, Mykola Dudkin, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-29535-0
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
Control code
978-3-319-29535-0
Dimensions
unknown
Extent
1 online resource (XX, 237 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319295350
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-29535-0
Other physical details
1 illustration.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)953455878
Label
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, by Volodymyr Koshmanenko, Mykola Dudkin, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-29535-0
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
Control code
978-3-319-29535-0
Dimensions
unknown
Extent
1 online resource (XX, 237 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319295350
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-29535-0
Other physical details
1 illustration.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)953455878

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