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Classes of uniform convergence of spectral expansions for the one-dimensional Schrödinger operator with a distribution potential

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Abstract

For the self-adjoint Schrödinger operator ℒ defined on ℝ by the differential operation −(d/dx)2 + q(x) with a distribution potential q(x) uniformly locally belonging to the space W 2 −1, we describe classes of functions whose spectral expansions corresponding to the operator ℒ absolutely and uniformly converge on the entire line ℝ. We characterize the sharp convergence rate of the spectral expansion of a function using a two-sided estimate obtained in the paper for its generalized Fourier transforms.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119992, Russia

    L. V. Kritskov

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  1. L. V. Kritskov
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Correspondence to L. V. Kritskov.

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Original Russian Text © L.V. Kritskov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 5, pp. 591–602.

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Kritskov, L.V. Classes of uniform convergence of spectral expansions for the one-dimensional Schrödinger operator with a distribution potential. Diff Equat 53, 583–594 (2017). https://doi.org/10.1134/S0012266117050020

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  • DOI: https://doi.org/10.1134/S0012266117050020

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