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L^p norms of non-critical Schrödinger semigroups

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.

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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).

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Simon, B.0000-0003-2561-8539
Additional Information:© 1991 Academic Press. Received 3 October 1990. Research partially funded under NSF Grant DMS-8801981.
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80943
Deposited By: Ruth Sustaita
Deposited On:30 Aug 2017 16:06
Last Modified:15 Nov 2021 19:39

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