Davies, E. B. and Simon, B. (1991) L^p norms of non-critical Schrödinger semigroups. Journal of Functional Analysis, 102 (1). pp. 95-115. ISSN 0022-1236. doi:10.1016/0022-1236(91)90137-T. https://resolver.caltech.edu/CaltechAUTHORS:20170830-081216215
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Abstract
We consider Schrödinger semigroups e^(−tH), H = −Δ + V on R^n with V ~ −c❘x❘^(−2), as ❘x❘ → ∞, 0 < c < [(12)(n−2)]^2, with H ⩾ 0. We determine the exact power law divergence of ∥e^(−tH)∥_(p,p) and of some ∥e^(−tH)∥_(q,p) as maps from L^p to L^q. The results are expressed most naturally in terms of the power α for which there exists a positive resonance η such that Hη = 0, η(x) ~ ❘x❘^(−α).
| Item Type: | Article | |||||||||
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| Additional Information: | © 1991 Academic Press. Received 3 October 1990. Research partially funded under NSF Grant DMS-8801981. | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1016/0022-1236(91)90137-T | |||||||||
| Record Number: | CaltechAUTHORS:20170830-081216215 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170830-081216215 | |||||||||
| Official Citation: | E.B Davies, B Simon, norms of non-critical Schrödinger semigroups, Journal of Functional Analysis, Volume 102, Issue 1, 1991, Pages 95-115, ISSN 0022-1236, http://dx.doi.org/10.1016/0022-1236(91)90137-T. (http://www.sciencedirect.com/science/article/pii/002212369190137T) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 80943 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 30 Aug 2017 16:06 | |||||||||
| Last Modified: | 15 Nov 2021 19:39 |
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