A general HELP inequality connected with symmetric operators

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, a general HELP (Hardy-Everitt-Littlewood-Pólya) inequality is considered which is connected with a symmetric operator in a Hilbert space and abstract boundary mappings. A criterion for the validity of such an inequality in terms of the abstract Titchmarsh-Weyl function is proved and applied to Sturm-Liouville operators, difference operators, a Hamiltonian system and a block operator matrix.
LanguageEnglish
Pages587-606
Number of pages20
JournalProceedings A: Mathematical, Physical and Engineering Sciences
Volume462
Issue number2066
Early online date13 Dec 2005
DOIs
Publication statusPublished - 2006

Fingerprint

Symmetric Operator
Mathematical operators
Weyl Function
operators
Sturm-Liouville Operator
Operator Matrix
Block Matrix
Difference Operator
Sturm-Liouville theory
Hamiltonian Systems
Hilbert space
Hamiltonians
Hilbert spaces

Keywords

  • HELP
  • boundary mappings
  • Titchmarsh-Weyl function
  • block operator matrix
  • numerical mathematics
  • inequality
  • copson’s inequality
  • hamiltonian system

Cite this

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title = "A general HELP inequality connected with symmetric operators",
abstract = "In this paper, a general HELP (Hardy-Everitt-Littlewood-P{\'o}lya) inequality is considered which is connected with a symmetric operator in a Hilbert space and abstract boundary mappings. A criterion for the validity of such an inequality in terms of the abstract Titchmarsh-Weyl function is proved and applied to Sturm-Liouville operators, difference operators, a Hamiltonian system and a block operator matrix.",
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pages = "587--606",
journal = "Proceedings A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
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A general HELP inequality connected with symmetric operators. / Langer, M.

In: Proceedings A: Mathematical, Physical and Engineering Sciences, Vol. 462, No. 2066, 2006, p. 587-606.

Research output: Contribution to journalArticle

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KW - block operator matrix

KW - numerical mathematics

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KW - copson’s inequality

KW - hamiltonian system

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