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The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators

All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-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.

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Series Title
Operator Theory: Advances and Applications
Call Number
-
Publisher
Birkhäuser Cham : Birkhäuser Cham.,
Collation
XX, 237
Language
English
ISBN/ISSN
978-3-319-29535-0
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
-
Edition
-
Subject(s)
Mathematical Physics
Specific Detail Info
-
Statement of Responsibility
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Cataloger
Jemadi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-29535-0.pdf?pdf=button
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