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Negative powers of a singular Schrödinger operator and convergence of spectral decompositions

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Abstract

We compare theL 2(ℝN)-norms of negative powers of various Laplace and Schrödinger operators possessing a singular potential whose singularities lie on some manifolds. We write out sufficient conditions for uniform convergence and localization of spectral decompositions of functions from the Liouville class.

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Authors and Affiliations

  1. Tashkent State University, USSR

    A. R. Khalmukhamedov

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  1. A. R. Khalmukhamedov
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Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 428–436, March, 1996.

The author wishes to express deep gratitude to Prof. Sh. A. Alimov for his attention to this work.

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Khalmukhamedov, A.R. Negative powers of a singular Schrödinger operator and convergence of spectral decompositions. Math Notes 59, 303–309 (1996). https://doi.org/10.1007/BF02308543

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  • DOI: https://doi.org/10.1007/BF02308543

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