×

zbMATH — the first resource for mathematics

Weyl asymptotics for the phase in obstacle scattering. (English) Zbl 0686.35089
In this note it is proved that Weyl’s asymptotic formula holds for the scattering phase.
Reviewer: J.Tian

MSC:
35P25 Scattering theory for PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bardos C., Application à la theéorie de la diffusion, Comm. P.D.E 7 pp 905– (1982) · Zbl 0496.35067
[2] Buslaev V.S., Dokl. Akad. Nauk Ussr 197 pp 1067–
[3] Duistermaat J.J., Invent. Math 29 pp 39– (1975) · Zbl 0307.35071
[4] Helton J.W., J.Diff. Eqn 21 pp 378– (1976) · Zbl 0343.35069
[5] Hörmander, L. 1983. ”The Analysis of Linear Partial Differential Operators III”. Heidelberg: Springer–Verlag. · Zbl 0521.35002
[6] Ivrii V.Ja., Funkcional. anal. i Prilozen 14 (2) pp 25– (1980)
[7] Jensen A., Comm. in P.D.E 3 (12) pp 1165– (1978) · Zbl 0419.35067
[8] Lax P.D., Advances in Math.Suppl. Studies 3 pp 197– (1978)
[9] Majda A., Duke Math. J. 45 pp 183– (1978) · Zbl 0408.35069
[10] Melrose R.B., J. Funct. Anal. 53 pp 287– (1983) · Zbl 0535.35067
[11] R.B. Melrose,Polynomial bound on the distribution of poles in scattering by an obstacle, in ”Journées ’Equations aux dérivées partielles’ Saint–Jean–de–monts,” 1984.
[12] R.B. Melrose, Growth estimates for th poles in potential scattering, Unpublished.
[13] Melrose R.B., Comm. Pure Appl.Math. 35 pp 129– (1982) · Zbl 0546.35083
[14] Petkov V., Ann. Inst. Four 32 (3) pp 111– (1982) · Zbl 0476.35014
[15] Seeley R.T., Amer. J. Math. 102 pp 869– (1980) · Zbl 0447.35029
[16] Zworski M., J. Funct. Anal. 73 pp 277– (1987) · Zbl 0662.34033
[17] M.Zworski, Sharp polynomial bounds on the number of scattering poles of radial potentials, J. Funct. Anal. (to appear). · Zbl 0681.47002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.