Published July 1981
| public
Journal Article
Spectrum and continuum eigenfunctions of Schrödinger operators
- Creators
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Simon, Barry
Abstract
We consider Schrödinger operators H = −1/2 Δ + V for a large class of potentials. V. We show that if Hϕ = Eϕ has a polynomially bounded solution ϕ then E is in the spectrum of H. This is accomplished by proving that the spectrum of H as an operator on L^2 is identical to its spectrum as an operator on the weighted L^2 space, L^2_δ.
Additional Information
© 1981 Published by Elsevier. Received November 19. 1980; revised December 2, 1980. Communicated by Peter D. Lax. research partially supported by USNSF under Grant MCS-78-21885. It is a pleasure to thank B. Souiliard for raising the question of converses to Theorem 1.1.Additional details
- Eprint ID
- 86525
- Resolver ID
- CaltechAUTHORS:20180521-152345997
- MCS-78-21885
- NSF
- Sherman Fairchild Foundation
- Created
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2018-05-21Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field