Sharp polynomial bounds on the number of scattering poles. (English) Zbl 0705.35099

Zworski, Maciej

Duke Math. J. 59, No. 2, 311-323 (1989).

Es wird die Streumatrix S(\(\lambda\)) untersucht für \(H_ 0=-\Delta\), \(H=-\Delta +V\) mit beschränktem meßbaren V mit kompaktem Träger in \({\mathbb{R}}^ n\) (n ungerade). Für N(r), die Zahl der Pole \(\lambda_ j\) der Streumatrix mit \(| \lambda_ j| \leq r\) wird die scharfe Abschätzung \(N(r)\leq C+Cr^ n\) bewiesen. Der Beweis ergibt sich durch eine Verbindung von Resultaten von R. Melrose und einer Determinantenformel aus der physikalischen Streutheorie.

Reviewer: J.Weidmann

MSC:

35P25	Scattering theory for PDEs
35J10	Schrödinger operator, Schrödinger equation

Keywords:

scattering matrix; number of scattering poles

References:

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