On Spectral Properties of the Acoustic Propagator in a Layered Band

✍ Scribed by Matania Ben-Artzi

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 390 KB
• Volume: 136
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.3236

✦ Synopsis

The acoustic propagator is the self-adjoint operator H=&{ } c(x) 2 {, defined in L 2 (Q), where Q R 2 is a band of finite width, given by Q=[(x, z), x # R, 0 z 1]. The wave velocity c depends only on the horizontal coordinate x, and is a measurable bounded function, converging to c \ >0 as x Ä \ .

It is proved that the resolvent operator R(z)=(H&z) &1 , Im z{0, can be extended continuously to the closed upper (or lower) half-plane, in a suitable weighted-L 2 topology (``Limiting Absorption Principle''). In particular, this continuity holds at the threshold *=0. It follows as a corollary that H has no point spectrum.