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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on solutions of the Schrödinger equation


Author: Wolfhard Hansen
Journal: Proc. Amer. Math. Soc. 117 (1993), 381-384
MSC: Primary 35J10; Secondary 35A20, 35B05
MathSciNet review: 1107921
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Abstract: Using a suitable geometric series a simple proof for the continuity of $ {L^1}$-solutions of the Schrödinger equation $ Lu: = \Delta u - Vu$ ($ V$ being a Kato function) is obtained. It works as well for uniformly elliptic operators having Hölder continuous coefficients and Kato measures instead of Kato functions. Moreover, it is shown that results on singularities are immediate consequences of the local existence of continuous Green functions for $ L$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1107921-1
PII: S 0002-9939(1993)1107921-1
Keywords: Schrödinger equation, isolated singularity, Kato function, Kato measure
Article copyright: © Copyright 1993 American Mathematical Society