TY - JOUR
T1 - An application of asymptotic techniques to certain problems of spectral and scattering theory of stark-like hamiltonians
AU - Ben-Artzi, Matania
PY - 1983/8
Y1 - 1983/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=17244379892&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1983-0701525-6
DO - 10.1090/S0002-9947-1983-0701525-6
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AN - SCOPUS:17244379892
SN - 0002-9947
VL - 278
SP - 817
EP - 839
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -