An application of asymptotic techniques to certain problems of spectral and scattering theory of stark-like hamiltonians

Matania Ben-Artzi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Let (FORMAL PRESENTED) be selfadjoint in L2(Rn). Here K, Vp are real functions, K(x,) depends only on the first coordinate. Existence of the wave-operators (FORMAL PRESENTED) is proved, using the stationary phase method. For this, an asymptotic technique is applied to the study of -d2/dt2 + V(t) in L2(R). Its absolute continuity is proved as well as a suitable eigenfunction expansion. V is a “Stark-like” potential. In particular, the cases (FORMAL PRESENTED), are included. Vp may be taken as the sum of an L2-function and a function satisfying growth conditions in the +X1 direction. (FORMAL PRESENTED)is included.

Original languageEnglish
Pages (from-to)817-839
Number of pages23
JournalTransactions of the American Mathematical Society
Volume278
Issue number2
DOIs
StatePublished - Aug 1983
Externally publishedYes

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