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Asymptotic distribution of resonances in one dimension. (English) Zbl 0955.35057
Summary: We determine the leading asymptotics of the resonance counting function for a class of Schrödinger operators in one dimension whose potentials may have non-compact support, i.e. is super-exponentially decreasing.

MSC:
35P20Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
35J10Schrödinger operator
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
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References:
[1] Jr., Ralph Philip Boas: Entire functions. (1954)
[2] Cooper, J.; Perla-Menzala, G.; Strauss, W.: On the scattering frequencies of time-dependent potentials. Math. meth. Appl. sci. 8, 576-584 (1986) · Zbl 0626.35074
[3] Levin, B. Ja.: Distribution of zeros of entire functions. American mathematical society translations of mathematical monographs 5 (1964)
[4] Müller, W.: Spectral geometry and scattering theory for certain complete surfaces of finite volume. Invent. math. 109, 265-305 (1992) · Zbl 0772.58063
[5] Antônio, Sà, Barreto, Maciej, Zworski, Existence of resonances in three dimensions · Zbl 0835.35099
[6] Simon, Barry: Trace ideals and their applications. London mathematical society lecture note series 35 (1979) · Zbl 0423.47001
[7] Titchmarsh, E. C.: The zeros of certain classes of integral functions. Proc. London math. Soc. 25, 283-302 (1926) · Zbl 52.0334.03
[8] Maciej, Zworski, Counting scattering poles, Spectral and Scattering Theory, Dekker, New York · Zbl 0705.35099
[9] Zworski, Maciej: Distribution of poles for scattering on the real line. J. funct. Anal. 73, 277-296 (1987) · Zbl 0662.34033
[10] Zworski, Maciej: Sharp polynomial bounds on the number of scattering poles of radial potentials. J. funct. Anal. 82, 370-403 (1989) · Zbl 0681.47002
[11] Zworski, Maciej: Sharp polynomial bounds on the number of scattering poles. Duke math. J. 59, 311-323 (1989) · Zbl 0705.35099