zbMATH — the first resource for mathematics

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.

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
Full Text: DOI
[1] Boas, Ralph Philip, Entire functions, (1954), 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, American mathematical society translations of mathematical monographs, 5, (1964), Am. Math. Soc Providence
[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), Cambridge Univ. Press Cambridge
[7] Titchmarsh, E.C., The zeros of certain classes of integral functions, Proc. London math. soc., 25, 283-302, (1926) · JFM 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
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.