Sharp bounds on the number of scattering poles for perturbations of the Laplacian. (English) Zbl 0766.35032

Vodev, Georgi

Commun. Math. Phys. 146, No. 1, 205-216 (1992).

Author’s summary: Sharp bounds on the number \(N(r)\) of the scattering poles in the disc \(| z|\leq r\) for large class of compactly supported perturbations (not necessarily selfadjoint) of the Laplacian in \(\mathbb{R}^ n\), \(n\geq 3\), odd, are obtained. In particular, in the elliptic case the estimate \(N(r)\leq Cr^ n+C\) is proved.

Reviewer: B.D.Sleeman (Dundee)

MSC:

35P25	Scattering theory for PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
47A40	Scattering theory of linear operators

Keywords:

odd dimensional space; compactly supported perturbations

References:

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