Froese, Richard Asymptotic distribution of resonances in one dimension. (English) Zbl 0955.35057 J. Differ. Equations 137, No. 2, 251-272 (1997). 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. Cited in 1 ReviewCited in 52 Documents MSC: 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35J10 Schrödinger operator, Schrödinger equation 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis Keywords:zeros of entire functions; super-exponentially decreasing; resonance counting function PDF BibTeX XML Cite \textit{R. Froese}, J. Differ. Equations 137, No. 2, 251--272 (1997; Zbl 0955.35057) Full Text: DOI References: [1] Boas, Ralph Philip, Entire Functions (1954), Academic Press: Academic Press San Diego · Zbl 0058.30201 [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. Distribution of Zeros of Entire Functions, American Mathematical Society Translations of Mathematical Monographs, 5 (1964), Am. Math. Soc: Am. Math. Soc Providence · Zbl 0152.06703 [4] Müller, W., Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. Math., 109, 265-305 (1992) · Zbl 0772.58063 [6] Simon, Barry, Trace Ideals and Their Applications. Trace Ideals and Their Applications, London Mathematical Society Lecture Note Series 35 (1979), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0423.47001 [7] Titchmarsh, E. C., The zeros of certain classes of integral functions, Proc. London Math. Soc., 25, 283-302 (1926) · JFM 52.0334.03 [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 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.