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Sharp bounds on the number of scattering poles in even-dimensional spaces

Georgi Vodev
Source: Duke Math. J. Volume 74, Number 1 (1994), 1-17.
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Primary Subjects: 35P25
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288007
Mathematical Reviews number (MathSciNet): MR1271461
Zentralblatt MATH identifier: 0813.35075
Digital Object Identifier: doi:10.1215/S0012-7094-94-07401-2

References

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Mathematical Reviews (MathSciNet): MR87j:35286
Zentralblatt MATH: 0607.35069
Digital Object Identifier: doi:10.1080/03605308608820428
[2] A. Intissar, On the value distribution of the scattering poles associated to the Schrödinger operator $H=(--i\nabla+b(x))^2+a(x)$ in $\mathbf R^n, n\geqslant3$, preprint.
[3] P. D. Lax and R. S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York, 1967.
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[4] B. Ja. Levin, Distribution of Zeros of Entire Functions, Trans. Math. Monographs, vol. 5, Amer. Math. Soc., Providence, R.I., 1964.
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[5] R. Melrose, Polynomial bound on the number of scattering poles, J. Funct. Anal. 53 (1983), no. 3, 287–303.
Mathematical Reviews (MathSciNet): MR85k:35180
Zentralblatt MATH: 0535.35067
Digital Object Identifier: doi:10.1016/0022-1236(83)90036-8
[6] R. B. Melrose, Polynomial bounds on the distribution of the poles in scattering by obstacle, Journées “Equations aux Dérivées partielles”, Saint-Jean-de-Montes, 1984.
Zentralblatt MATH: 0621.35073
[7] R. B. Melrose, Weyl asymptotics for the phase in obstacle scattering, Comm. Partial Differential Equations 13 (1988), no. 11, 1431–1439.
Mathematical Reviews (MathSciNet): MR90a:35183
Zentralblatt MATH: 0686.35089
Digital Object Identifier: doi:10.1080/03605308808820582
[8] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), no. 4, 729–769.
Mathematical Reviews (MathSciNet): MR92g:35166
Zentralblatt MATH: 0752.35046
Digital Object Identifier: doi:10.2307/2939287
[9] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, Comm. Partial Differential Equations 18 (1993), no. 5-6, 847–857.
Mathematical Reviews (MathSciNet): MR94h:35198
Zentralblatt MATH: 0784.35070
Digital Object Identifier: doi:10.1080/03605309308820953
[10] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II, J. Functional AnaL., to appear.
Mathematical Reviews (MathSciNet): MR1283032
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[11] B. R. Vainberg, Asymptotic methods in equations of mathematical physics, Gordon & Breach Science Publishers, New York, 1989.
Mathematical Reviews (MathSciNet): MR91h:35081
Zentralblatt MATH: 0743.35001
[12] G. Vodev, Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in $\bf R\sp n$, Math. Ann. 291 (1991), no. 1, 39–49.
Mathematical Reviews (MathSciNet): MR93f:47060
Zentralblatt MATH: 0754.35105
Digital Object Identifier: doi:10.1007/BF01445189
[13] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), no. 1, 205–216.
Mathematical Reviews (MathSciNet): MR93f:35173
Zentralblatt MATH: 0766.35032
Digital Object Identifier: doi:10.1007/BF02099213
Project Euclid: euclid.cmp/1104249981
[14] M. Zworski, Sharp polynomial bounds on the number of scattering poles of radial potentials, J. Funct. Anal. 82 (1989), no. 2, 370–403.
Mathematical Reviews (MathSciNet): MR90d:35233
Zentralblatt MATH: 0681.47002
Digital Object Identifier: doi:10.1016/0022-1236(89)90076-1
[15] M. Zworski, Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), no. 2, 311–323.
Mathematical Reviews (MathSciNet): MR90h:35190
Zentralblatt MATH: 0705.35099
Digital Object Identifier: doi:10.1215/S0012-7094-89-05913-9
Project Euclid: euclid.dmj/1077308003
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