Finite rank perturbations and distribution theory

Proceedings of the American Mathematical Society

Volumn 127, Issue 4, 1999, Pages 1151-1161

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

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b Sfb 237 Essen Bochum DüSseldorf ^*  (Germany)

^c BIELEFELD UNIVERSITY   (Germany)

^d CERFIM   (Switzerland)

^e UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644450942     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04992-8     Document Type: Article

References (19)

1. N.I.Akhiezer, I.M.Glazman, " Theory of linear operators in Hubert Space" , vol I, II, Pitman, London, 1981. MR 831:47001
2. S.Albeverio, F.Gesztesy, R.Hoegh-Krohn, H.Holden, " Solvable models in quantum mechanics" , Springer-Verlag, 1988. MR 90a:81021
3. S.Albeverio, W.Kanvowski, V.Koshmanenko, Square powers of singularly perturbed operators, Math. Nachr. 173, 5-24 (1995). MR 97a:47035
4. S.Albeverio, V.Koshmanenko, Some remarks on the Gesztesy-Simon version of rank one perturbations, Kiev Preprint (1996).
5. S.Albeverio, P.Kurasov, Rank one perturbations, approximations and selfadjoint extensions, J. Func. Anal. 148, 152-169 (1997). MR 98g:47011
6. S.Albeverio, P.Kurasov, Rank one perturbations of not semibounded operators, Integr. Eq. Oper. Theory 27, 379-400 (1997). CMP 97:10
7. S.Albeverio, P.Kurasov, " Solvable Schrödinger type operators. Singular perturbations of differential operators" , Cambridge Univ. Press, to appear.
8. J.Boman, P.Kurasov, Finite Rank Singular Perturbations and Distributions with Discontinuous Testfunctions, Proceedings AMS 126 (1998), 1673-1683. MR 98g:47012
9. F.Gesztesy and B.Simon, Rank one perturbations at infinite coupling, J. Func. Anal 128, 245-252 (1995). MR 95m:47014
10. S.Hassi, H.Langer, H. de Snoo, Selfadjoint extensions for a class of symmetric operators with defect numbers (1,1), in: A.Gheondea, S.Stratila, D. Timotin (eds.), " Topics in Operator Theory, Operator Algebras and Applications" , Inst. of Mathematics of the Romanian Academy, Bucharest, 1995, pp. 115-145. MR 97m:47024
11. S.Hassi, H. de Snoo, On rank one perturbations of selfadjoint operators, Integr. Eq. Oper. Theory 29, 288-300 (1997). CMP 98:03
12. L.Hormander, " The Analysis of Linear Partial Differential Operators I" , Springer-Verlag, Berlin, 1983. MR 85g:35002a
13. A.Kiselev, and B.Simon, Rank one perturbations with infinitesimal coupling, J. Func. Anal 130, 345- 356 (1995). MR 96e:47012
14. V.D.Koshmanenko, Toward the Rank-one Singular Perturbations Theory of Self-adjoint Operators, Ukranian Math. J. 43, No 11, 1450-1457 (1991). MR 93b:47020
15. P.Kurasov, Distribution theory for the discontinuous test functions and differential operators with the generalized coefficients, J.Math. Anal. Appl. 201, 297-323 (1996) . MR 97g:46050
16. P.Kurasov, Rank one perturbations of nonsemibounded operators, Research report 1995-15, Luleâ University of Technology, Lulea, Sweden, 1995.
17. M.G.Krein, Concerning the resolvents of an Hermitian operator with the deficiency-index (m,m), C. R. (Dokl.) Akad. Sei. URSS 52, 651-654 (1946). MR 8:277a
18. M.Reed, B.Simon, " Methods of modern mathematical physics" , vol. II, Academic Press, New York, 1975. MR 58:12429b
19. B.Simon, Spectral Analysis of Rank One Perturbations and Applications, CRM Proceedings and Lecture Notes, Volume 8, 109-149 (1995). MR 97c:47008