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Unbounded Hermitian operators and relative reproducing kernel Hilbert space
Journal article   Peer reviewed

Unbounded Hermitian operators and relative reproducing kernel Hilbert space

Open Mathematics, Vol.8(3), pp.569-596
06/01/2010
DOI: 10.2478/s11533-010-0021-8
url
https://doaj.org/article/b4b3d330472b424eb7acf730d6f17a15View
Open Access

Abstract

We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.
Reproducing kernel Function spaces 47B25 47B37 81P15 47B32 Hilbert space 81Q10 47S50 Linear operator 60H25

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