Lower bounds on the number of scattering poles. II. (English) Zbl 0823.35137

Sjöstrand, Johannes; Zworski, Maciej

J. Funct. Anal. 123, No. 2, 336-367 (1994).

In continuation of their paper [Commun. Partial Differ. Equ. 18, No. 5-6, 847-857 (1993; Zbl 0784.35070)] (where several examples were treated), here the authors obtain a very general lower bound on the number of scattering poles, for a wide class of abstract compactly supported perturbations of the Laplacian in \(\mathbb{R}^ n\) (\(n\) odd). The proof is based on the exploitation of the singularities of the wave trace at zero.

Reviewer: A.Martinez (Villetaneuse)

MSC:

35P25	Scattering theory for PDEs
35P15	Estimates of eigenvalues in context of PDEs
47A40	Scattering theory of linear operators

Keywords:

resonances; scattering poles

Citations:

Zbl 0784.35070