The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators (eBook, PDF)

The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators (eBook, PDF)

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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 d-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 singul...

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