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Uniform, on the entire axis, convergence of the spectral expansion for Schrödinger operator with a potential-distribution

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Abstract

A uniform, on ℝ, estimate for the increment of the spectral function θ(λ; x, y) at x = y is proved for the self-adjoint Schrödinger operator A defined on the entire axis ℝ by the differential operation (−d/dx)2 + q(x) with a potential-distribution q(x) that uniformly locally belongs to the space W 2 −1. As a consequence, it is shown that for any function f(x) from the domain of power Aα of the operator with α > 1/4, the spectral expansion of the function that corresponds to the operator A is convergent absolutely and uniformly on the entire axis ℝ.

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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. 2, pp. 183–194.

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Kritskov, L.V. Uniform, on the entire axis, convergence of the spectral expansion for Schrödinger operator with a potential-distribution. Diff Equat 53, 180–191 (2017). https://doi.org/10.1134/S0012266117020045

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