An application of asymptotic techniques to certain problems of spectral and scattering theory of Stark-like Hamiltonians

Author:
Matania Ben-Artzi

Journal:
Trans. Amer. Math. Soc. **278** (1983), 817-839

MSC:
Primary 35P25; Secondary 81C10

DOI:
https://doi.org/10.1090/S0002-9947-1983-0701525-6

MathSciNet review:
701525

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Abstract: Let be selfadjoint in . Here are real functions, depends only on the first coordinate. Existence of the wave-operators - is proved, using the stationary phase method. For this, an asymptotic technique is applied to the study of in . Its absolute continuity is proved as well as a suitable eigenfunction expansion. is a "Stark-like" potential. In particular, the cases , are included. may be taken as the sum of an -function and a function satisfying growth conditions in the direction. is included.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0701525-6

Article copyright:
© Copyright 1983
American Mathematical Society