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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