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Rank One Perturbations with Infinitesimal Coupling

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.

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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.

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Simon, B.0000-0003-2561-8539
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
Record Number:CaltechAUTHORS:20170906-141427255
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81199
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 21:29
Last Modified:15 Nov 2021 19:41

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