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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On approximations of rank one ${\mathcal H}_{-2}$-perturbations


Authors: S. Albeverio, V. Koshmanenko, P. Kurasov and L. Nizhnik
Journal: Proc. Amer. Math. Soc. 131 (2003), 1443-1452
MSC (2000): Primary 47A55, 47B25; Secondary 81Q15
Published electronically: September 5, 2002
MathSciNet review: 1949874
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Abstract: Approximations of rank one ${\mathcal H}_{-2}$-perturbations of self-adjoint operators by operators with regular rank one perturbations are discussed. It is proven that in the case of arbitrary not semibounded operators such approximations in the norm resolvent sense can be constructed without any renormalization of the coupling constant. Approximations of semibounded operators are constructed using rank one non-symmetric regular perturbations.


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Additional Information

S. Albeverio
Affiliation: Institute für Angewandte Mathematik, Univ. Bonn, Wegelerstr. 6, 53155 Bonn, Germany; SFB 256 Bonn, BiBoS, Bielefeld-Bonn, CERFIM, Locarno and USI (Switzerland)
Email: albeverio@uni-bonn.de

V. Koshmanenko
Affiliation: Institute of Mathematics, vul. Tereschenkivs’ka, 3, Kyiv, 01601 Ukraine
Email: kosh@imath.kiev.ua

P. Kurasov
Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
Address at time of publication: Department of Mathematics, Lund Institute of Technology, Box 118, 221 00 Lund, Sweden
Email: pak@matematik.su.se, kurasov@maths.lth.se

L. Nizhnik
Affiliation: Institute of Mathematics, vul. Tereschenkivs’ka, 3, Kyiv, 01601 Ukraine
Email: nizhnik@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06694-7
PII: S 0002-9939(02)06694-7
Keywords: Self-adjoint operators, singular interactions
Received by editor(s): July 19, 2001
Received by editor(s) in revised form: December 7, 2001
Published electronically: September 5, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society