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About this product
- DescriptionThis mograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key tion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into ather, which specifies the well-kwn Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac delta-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 canical 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 phemen, and singular interaction problems.
- Author(s)Volodymyr Koshmanenko
- PublisherBirkhauser Verlag AG
- Date of Publication19/04/2016
- Series TitleOperator Theory: Advances and Applications
- Series Part/Volume Number253
- Place of PublicationBasel
- Country of PublicationSwitzerland
- ImprintBirkhauser Verlag AG
- Content Note1 black & white illustrations, biography
- Weight555 g
- Width155 mm
- Height235 mm
- Edition Statement2016 ed.
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