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Singular quadratic forms in perturbation theory

Author: V D Koshmanenko
Publisher: Dordrecht ; Boston : Kluwer, ©1999.
Series: Mathematics and its applications (Kluwer Academic Publishers), v. 474.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This monograph is devoted to the systematic presentation of the method of singular quadratic forms in the perturbation theory of self-adjoint operators." "The concept of a singular (nowhere closable) quadratic form, a key notion of the present volume, is treated from different points of view such as definition, properties, relations with regular (closable) quadratic forms, operator representation, classification in  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V D Koshmanenko
ISBN: 079235625X 9780792356257
OCLC Number: 40693831
Description: viii, 308 pages ; 25 cm.
Contents: Ch. 1. Quadratic Forms and Linear Operators --
1. Preliminary Facts about Quadratic Forms --
2. Closed and Closable Quadratic Forms --
3. Operator Representations of Quadratic Forms --
4. Quadratic Forms in the Theory of Self-Adjoint Extensions of Symmetric Operators --
Ch. 2. Singular Quadratic Forms --
5. Definition of Singular Quadratic Forms --
6. Properties of Singular Quadratic Forms --
7. Operator Representation of Singular Quadratic Forms --
8. Singular Quadratic Forms in the A-Scale of Hilbert Spaces --
9. Regularization --
Ch. 3. Singular Perturbations of Self-Adjoint Operators --
10. Rank-One Singular Perturbations --
11. Singular Perturbations of Finite Rank --
12. Method of Self-Adjoint Extensions --
13. Powers of Singularly Perturbed Operators --
14. Method of Orthogonal Extensions --
15. Approximations --
Ch. 4. Applications to Quantum Field Theory --
16. Singular Properties of Wick Monomials --
17. Orthogonally Extended Fock Space --
18. Scattering and Spectral Problems.
Series Title: Mathematics and its applications (Kluwer Academic Publishers), v. 474.
Other Titles: Singuli︠a︡rnye bilineĭnye formy v teorii vozmushcheniĭ samosopri︠a︡zhennykh operatorov.
Responsibility: by Volodymyr Koshmanenko.
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Abstract:

The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense.  Read more...

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` ...this text is a valuable contribution to the literature on the abstract aspects of singular perturbation theory.' Mathematical Reviews, 2001a

 
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