Rank one perturbations, approximations, and selfadjoint extensions

Journal of Functional Analysis

Volumn 148, Issue 1, 1997, Pages 152-169

  Albeverio, S ^a,b,c,d   Kurasov, P ^a,e,f  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b SFB 237 ^*  (Germany)

^c BIELEFELD UNIVERSITY   (Germany)

^d CERFIM   (Switzerland)

^e ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^f LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031212486     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.3050     Document Type: Article

References (18)

1. Albeverio S., Gesztesy F., Høegh-Krohn R., Holden H. Solvable Models in Quantum Mechanics. 1988;Springer-Verlag, Berlin/New York.
2. Albeverio S., Karwowski W., Koshmanenko V. Square power of singularly perturbed operators. Math. Nachr. 173:1995;5-24.
3. S. Albeverio, V. Koshmanenko, 1996, Some remarks on the Gesztesy-Simon version of rank one perturbations.
4. Albeverio S., Kurasov P. Rank one perturbations of not semibounded operators. J. Integral Equations Oper. Theory. 27:1997;379-400.
5. Alonso A., Simon B. The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. J. Operator Theory. 4:1980;251-270.
6. Beresin F. A., Faddeev L. D. A remark on Schrödinger equation with a singular potential. Sov. Math. Dokl. 137:1961;1011-1014.
7. J. Boman, P. Kurasov, Finite rank singular perturbations and distributions with discontinuous test functions.
8. Birman M. S. On the self-adjoint extensions of positive definite operators. Math. Sb. 38:1956;431-456.
9. Gesztesy F., Simon B. Rank one perturbations at infinite coupling. J. Funct. Anal. 128:1995;245-252.
10. H. Hassi, H. de Snoo, On rank one perturbations of selfadjoint operators.
11. Hörmander L. The Analysis of Linear Partial Differential Operators, I. 1983;Springer-Verlag, Berlin.
12. Kiselev A., Simon B. Rank one perturbations with infinitesimal coupling. J. Funct. Anal. 130:1995;345-356.
13. Koshmanenko V. D. Towards the rank one singular perturbations theory of selfadjoint operators. Ukrainian Math. J. 43:1991;1559-1566.
14. Krein M. The theory of self-adjoint extensions of semibounded hermitian transformations and its applications, I. Rec. Math. (Math. Sb.). 20:1947;431-495.
15. Kurasov P. Distribution theory for the discontinuous test functions and differential operators with the generalized coefficients, preprint. J. Math. Anal. Appl. 1994.
16. Kurasov P. Research Report. 1995-15:1995.
17. Simon B. Spectral analysis of rank one perturbations and applications. CRM Proceedings and Lecture Notes. 1995;. p. 109-149.
18. Vishik M. On general boundary condition for elliptic differential equation. Trud. Moskov. Mat. Obshch. 1:1952;187-246.