A note on solutions of the Schrödinger equation
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- by Wolfhard Hansen
- Proc. Amer. Math. Soc. 117 (1993), 381-384
- DOI: https://doi.org/10.1090/S0002-9939-1993-1107921-1
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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 $L$.References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 381-384
- MSC: Primary 35J10; Secondary 35A20, 35B05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1107921-1
- MathSciNet review: 1107921