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Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm–Liouville Operators

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Perturbations of asymptotic decay c/r 2 arise in the partial-wave analysis of rotationally symmetric partial differential operators. We show that for each end-point λ0 of the spectral bands of a perturbed periodic Sturm–Liouville operator, there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at λ0 if and only if c/c crit>1. The oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near λ0.

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Received: 23 September 1999 / Accepted: 21 December 1999

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Schmidt, K. Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm–Liouville Operators. Comm Math Phys 211, 465–485 (2000). https://doi.org/10.1007/s002200050822

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  • DOI: https://doi.org/10.1007/s002200050822

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