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Expansion in characteristic functions of the Schrödinger operator with a singular potential

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Abstract

We study the spectral function of the operator −δ+v(x) in three-dimensional space, where v(x) is measurable and belongs to L2. We study the differentiability of this function with respect to some measure. Simultaneously, we give estimates of the characteristic functions of a continuous spectrum at infinity. This justifies the decomposition of an arbitrary function in terms of the characteristic functions of an operator with this type of potential.

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Authors and Affiliations

  1. Khar'kov Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR, Ukraine

    G. N. Gestrin

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  1. G. N. Gestrin
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Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 455–465, March, 1974.

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Gestrin, G.N. Expansion in characteristic functions of the Schrödinger operator with a singular potential. Mathematical Notes of the Academy of Sciences of the USSR 15, 266–272 (1974). https://doi.org/10.1007/BF01438382

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  • DOI: https://doi.org/10.1007/BF01438382

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