Operator Theory: Advances and Applications

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

Authors: Koshmanenko, Volodymyr, Dudkin, Mykola

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  • Deals with singular quadratic forms and singular perturbations of self-adjoint operators considered in rigged Hilbert spaces
  • Demonstrates the theory of singular perturbations by three notions into a unique object with a three-face image existing in the rigged Hilbert space
  • Provides an adequate tool for exploration of the singular perturbation problem
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Hardcover $139.99
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Softcover $139.99
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About this book

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 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.

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-29535-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-29533-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-80592-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
Authors
Translated by
Koshmanenko, N.
Series Title
Operator Theory: Advances and Applications
Series Volume
253
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29535-0
DOI
10.1007/978-3-319-29535-0
Hardcover ISBN
978-3-319-29533-6
Softcover ISBN
978-3-319-80592-4
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XX, 237
Number of Illustrations
1 b/w illustrations
Additional Information
Original Ukrainian edition published by Institute of Mathematics, NAS of Ukraine, Kyiv, 2013
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