Unbounded Hermitian operators and relative reproducing kernel Hilbert space

Palle Jorgensen

Open Mathematics (2010)

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

Abstract

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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.

How to cite

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Palle 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 -

References

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