Unbounded Hermitian operators and relative reproducing kernel Hilbert space

Palle Jorgensen

Open Mathematics, Tome 8 (2010), p. 569-596 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2010-01-01

Zbl 1220.47029

EUDML-ID : urn:eudml:doc:269727

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