Kiselev, A. and Simon, B. (1995) Rank One Perturbations with Infinitesimal Coupling. Journal of Functional Analysis, 130 (2). pp. 345-356. ISSN 0022-1236. doi:10.1006/jfan.1995.1074. https://resolver.caltech.edu/CaltechAUTHORS:20170906-141427255
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Abstract
We consider a positive self-adjoint operator A and formal rank one perturbations B = A + α(φ, ·)φ, where φ ∈ H−2(A) but φ ∉ H_(−1) (A), with H_s(A) the usual scale of spaces. We show that B can be defined for such φ and what are essentially negative infinitesimal values of α. In a sense we will make precise, every rank one perturbation is one of three forms: (i) φ ∈ H^(−1)(A), α ∈ R; (ii) φ ∈ H_(−1), α = ∞; or (iii) the new type we consider here.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1995 Academic Press. Received May 24, 1994. This material is based upon work supported by the National Science Foundation under Grant DMS-9101715. The Government has certain rights in this material. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1006/jfan.1995.1074 | |||||||||
| Record Number: | CaltechAUTHORS:20170906-141427255 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170906-141427255 | |||||||||
| Official Citation: | A. Kiselev, B. Simon, Rank One Perturbations with Infinitesimal Coupling, Journal of Functional Analysis, Volume 130, Issue 2, 1995, Pages 345-356, ISSN 0022-1236, http://dx.doi.org/10.1006/jfan.1995.1074. (http://www.sciencedirect.com/science/article/pii/S0022123685710749) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 81199 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 06 Sep 2017 21:29 | |||||||||
| Last Modified: | 15 Nov 2021 19:41 |
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