## The complex scaling method for scattering by strictly convex obstacles.(English)Zbl 0839.35095

The purpose of this paper is to obtain upper bounds for the number of scattering poles in varying neighborhoods of the real axis for scattering by strictly convex obstacles with $$C^\infty$$ boundaries. The new estimates generalize earlier results on the poles in small conic neighborhoods of the real axis by the authors [Ann. Inst. Fourier 43, No. 3, 769-790 (1993; Zbl 0784.35073)] and include the recent result of T. Hargé and G. Lebeau [Invent. Math. 118, No. 1, 161-196 (1994; Zbl 0831.35121)]. The proof is based on an ingenious choice of the angle of scaling appearing in Hargé-Lebeau and on the development of a new semi-classical reduction to the boundary partly inspired by the paper of the first author [Duke Math. J. 60, No. 1, 1-57 (1990; Zbl 0702.35188)].
Reviewer: B.Helffer (Orsay)

### MSC:

 35P25 Scattering theory for PDEs

### Keywords:

upper bounds for the number of scattering poles

### Citations:

Zbl 0784.35073; Zbl 0831.35121; Zbl 0702.35188
Full Text:

### References:

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