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Schrödinger semigroups on the scale of Sobolev spaces

Simon, Barry (1986) Schrödinger semigroups on the scale of Sobolev spaces. Pacific Journal of Mathematics, 122 (2). pp. 475-480. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:SIMpjm86

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Abstract

We consider the action of semigroups e(-tH), with H = -Δ + V on L(2)(R(v)), on the scale of Sobolev spaces H(α). We show that while e(-tH) maps L(2)=H(0) to H(2) under great generality, there exist bounded V so that, for all β > 0, e(-tH)[H(β)] is not contained in any H(α) with a > 2.


Item Type:Article
Additional Information:© 1986 Pacific Journal of Mathematics. Received December 17, 1984 and in revised form March 26, 1985. Research suported by USNSF under grant MCS-81-20833.
Record Number:CaltechAUTHORS:SIMpjm86
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SIMpjm86
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102701902
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:715
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Sep 2005
Last Modified:26 Dec 2012 08:41

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