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Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions

Carmona, René and Masters, Wen Chen and Simon, Barry (1990) Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions. Journal of Functional Analysis, 91 (1). pp. 117-142. ISSN 0022-1236. doi:10.1016/0022-1236(90)90049-Q.

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Nonrelativistic Schrödinger operators are perturbations of the negative Laplacian and the connection with stochastic processes (and Brownian motion in particular) is well known and usually goes under the name of Feynman and Kac. We present a similar connection between a class of relativistic Schrödinger operators and a class of processes with stationary independent increments. In particular, we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 1990 Published by Elsevier. Received December 19, 1988; received March 10, 1989. Communicated by L. Gross. Partially supported by NSF Grant DMS-8701320. Partially supported by NSF Grant DMS 84-16049. We thank E. Lieb for his comments on a first version of the paper. Moreover. the first named author (R.C.) thanks D. Bakry and S. Port for enlightening discussions on some of the facts of the theory of Lévy processes.
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NSFDMS 84-16049
Issue or Number:1
Record Number:CaltechAUTHORS:20180521-151747020
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Official Citation:René Carmona, Wen Chen Masters, Barry Simon, Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions, Journal of Functional Analysis, Volume 91, Issue 1, 1990, Pages 117-142, ISSN 0022-1236, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86523
Deposited By: George Porter
Deposited On:21 May 2018 22:32
Last Modified:15 Nov 2021 20:39

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