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The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
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 kin...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2016.
|
| Edición: | 1st ed. 2016. |
| Colección: | Operator Theory: Advances and Applications,
253 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-29535-0 | ||
| 003 | DE-He213 | ||
| 005 | 20220110191053.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 160708s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783319295350 |9 978-3-319-29535-0 | ||
| 024 | 7 | |a 10.1007/978-3-319-29535-0 |2 doi | |
| 050 | 4 | |a QA329-329.9 | |
| 072 | 7 | |a PBKF |2 bicssc | |
| 072 | 7 | |a MAT037000 |2 bisacsh | |
| 072 | 7 | |a PBKF |2 thema | |
| 082 | 0 | 4 | |a 515.724 |2 23 |
| 100 | 1 | |a Koshmanenko, Volodymyr. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 4 | |a The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators |h [electronic resource] / |c by Volodymyr Koshmanenko, Mykola Dudkin. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Birkhäuser, |c 2016. | |
| 300 | |a XX, 237 p. 1 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Operator Theory: Advances and Applications, |x 2296-4878 ; |v 253 | |
| 505 | 0 | |a Preface -- Introduction -- 1.Preliminaries -- 2.Symmetric Operators and Closable Quadratic Forms -- 3.Self-adjoint Extensions of Symmetric Operators -- 4.Rigged Hilbert Spaces -- 5.Singular Quadratic Forms -- 6.Dense Subspaces in Scales of Hilbert Spaces -- 7.Singular Perturbations of Self-adjoint Operators -- 8.Super-singular Perturbations -- 9.Some Aspects of the Spectral Theory -- References -- Subject Index -- Notation Index. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Measure and Integration. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 700 | 1 | |a Dudkin, Mykola. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319295336 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319295343 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319805924 |
| 830 | 0 | |a Operator Theory: Advances and Applications, |x 2296-4878 ; |v 253 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-29535-0 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||