Zworski, M. Counting scattering poles. (English) Zbl 0823.35139 Ikawa, Mitsuru (ed.), Spectral and scattering theory. Proceedings of the Taniguchi international workshop, held at Sanda, Hyogo, Japan. Basel: Marcel Dekker. Lect. Notes Pure Appl. Math. 161, 301-331 (1994). This survey describes the recent results on estimating the number of scattering poles, obtained by the author and J. Sjöstrand in joint works. For compactly supported perturbations of the Laplacian in \(\mathbb{R}^ n\), various upper bounds are obtained for the number of scattering poles inside conic-type regions of the complex plane, asymptotically as the diameter of these regions tends to infinity. Many other questions are discussed, such as the distribution of the poles near the real axis, and the obtention of lower bounds on their number. Also, several examples are discussed showing the accuracy (and sometimes the optimality) of the general results.For the entire collection see [Zbl 0798.00016]. Reviewer: A.Martinez (Villetaneuse) Cited in 17 Documents MSC: 35P25 Scattering theory for PDEs 81U20 \(S\)-matrix theory, etc. in quantum theory 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations Keywords:number of scattering poles; upper bounds; conic-type regions; distribution of the poles; lower bounds PDF BibTeX XML Cite \textit{M. Zworski}, Lect. Notes Pure Appl. Math. 161, 301--331 (1994; Zbl 0823.35139) OpenURL