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Invariant symmetric restrictions of a self-adjoint operator. II

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Abstract

We give a criterion of invariance and symmetry of the restriction of an arbitrary unbounded self-adjoint operator in the space L 2(ℝn, dx) by using the introduced notion of support of an arbitrary vector and the notion of capacity of a subspace N ⊂ ℝn.

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    M. E. Dudkin

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  1. M. E. Dudkin
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 781–791, June, 1998.

This work was partially supported by the Foundation for Fundamental Research of the Ministry of Science and Technology of the Ukraine (grant No. 1/238 “Operator”).

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Dudkin, M.E. Invariant symmetric restrictions of a self-adjoint operator. II. Ukr Math J 50, 888–900 (1998). https://doi.org/10.1007/BF02515222

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  • DOI: https://doi.org/10.1007/BF02515222

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