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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators

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

Koshmanenko, Volodymyr
Dudkin, Mykola
Koshmanenko, Nataliia

Hardcover

Series: Operator Theory: Advances and Applications, Book 253

General Mathematics

ISBN10: 3319295330
ISBN13: 9783319295336
Publisher: Springer Nature
Published: Jul 19 2016
Pages: 237
Weight: 1.19
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English

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.

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