Simon, Barry (1986) Schrödinger semigroups on the scale of Sobolev spaces. Pacific Journal of Mathematics, 122 (2). pp. 475-480. ISSN 0030-8730. https://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.
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| 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. | ||||||||||||
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| Issue or Number: | 2 | ||||||||||||
| Record Number: | CaltechAUTHORS:SIMpjm86 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:SIMpjm86 | ||||||||||||
| 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: | 02 Oct 2019 22:36 |
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