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Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions

Published online by Cambridge University Press:  20 November 2018

Richard Froese
Richard Froese*
Affiliation:
Department of Mathematics University of British Columbia Vancouver, BC V6T 1Z2
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Abstract

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The purpose of this note is to provide a simple proof of the sharp polynomial upper bound for the resonance counting function of a Schrödinger operator in odd dimensions. At the same time we generalize the result to the class of superexponentially decreasing potentials.

Keywords

47A1047A4081U05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 3 , 01 June 1998 , pp. 538 - 546
Copyright
Copyright © Canadian Mathematical Society 1998

References

[F] Froese, Richard, Asymptotic distribution of resonances in one dimension. J. Differential Equations (2) 137(1997), 251–272.Google Scholar
[Me1] Froese, Richard, Polynomial bound on the number of scattering poles. J. Funct. Anal. 53(1983), 287– 303.Google Scholar
[Me2] Froese, Richard, Geometric scattering theory. Cambridge University Press, Cambridge, 1995.Google Scholar
[S] Simon, Barry, Trace Ideals and their Applications. London Math. Soc. Lecture Note Ser. 35, Cambridge University Press, Cambridge, 1979.Google Scholar
[SZ1] Barreto, Antônio Sá and Zworski, Maciej, Existence of resonances in three dimensions. Comm. Math. Phys. (2) 173(1995), 401–415.Google Scholar
[SZ2] Barreto, Antônio Sá, Existence of resonances in potential scattering. Comm. Pure Appl. Math. (12) 49(1996), 1271– 1280.Google Scholar
[V] Vodev, Georgi, Sharp polynomial bounds on the number of scattering poles of perturbations of the Laplacian. Comm. Math. Phys. 146(1992), 205–216.Google Scholar
[Z1] Zworski, Maciej, Distribution of poles for scattering on the real line. J. Funct. Anal. (2) 73(1987), 277–296.Google Scholar
[Z2] Zworski, Maciej, Sharp polynomial bounds on the number of scattering poles of radial potentials. J. Funct. Anal. (2) 82(1989), 370–403.Google Scholar
[Z3] Zworski, Maciej, Sharp polynomial bounds on the number of scattering poles. Duke Math. J. (2) 59(1989), 311–323.Google Scholar
[Z4] Zworski, Maciej, Counting scattering poles. In: Spectral and scattering theory (Ed. M. Ikawa). Marcel Dekker, New York, 1994.Google Scholar