On spectral properties of the acoustic propagator in a layered band

[摘要] The acoustic propagator is the seIf-adjoint operator H=-V.c(x)(2) del, defined in L-2(Q), where Q subset of or equal to R-2 is a band of finite width, given by Q={(x,z), x is an element of R, 0 less than or equal to z less than or equal to Gamma}. The wave velocity a depends only on the horizontal coordinate x, and is a measurable bounded function, converging to c(divided by/-) >0 as x --> +/- infinity. It is proved that the resolvent operator R(z)=(H-Z)(-1), Imz=0, can Be extended continuously to the dosed upper (or lower) half-plane, in a suitable weighted-L-2 topology (''limiting Absorption Principle''). In particular, this continuity holds at the threshold lambda=0. It follows as a corollary that H has no point spectrum. (C) 1997 Academic Press.

[发布日期] 1997-05-01