# Unbounded Hermitian operators and relative reproducing kernel Hilbert space

Open Mathematics (2010)

- Volume: 8, Issue: 3, page 569-596
- ISSN: 2391-5455

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topPalle Jorgensen. "Unbounded Hermitian operators and relative reproducing kernel Hilbert space." Open Mathematics 8.3 (2010): 569-596. <http://eudml.org/doc/269727>.

@article{PalleJorgensen2010,

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.},

author = {Palle Jorgensen},

journal = {Open Mathematics},

keywords = {Hilbert space; Linear operator; Reproducing kernel; Function spaces; reproducing kernel Hilbert space; selfadjoint extensions; infinite weighted graph},

language = {eng},

number = {3},

pages = {569-596},

title = {Unbounded Hermitian operators and relative reproducing kernel Hilbert space},

url = {http://eudml.org/doc/269727},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Palle Jorgensen

TI - Unbounded Hermitian operators and relative reproducing kernel Hilbert space

JO - Open Mathematics

PY - 2010

VL - 8

IS - 3

SP - 569

EP - 596

AB - 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.

LA - eng

KW - Hilbert space; Linear operator; Reproducing kernel; Function spaces; reproducing kernel Hilbert space; selfadjoint extensions; infinite weighted graph

UR - http://eudml.org/doc/269727

ER -

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