A general HELP inequality connected with symmetric operators

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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.
Original languageEnglish
Pages (from-to)587-606
Number of pages20
JournalProceedings A: Mathematical, Physical and Engineering Sciences
Volume462
Issue number2066
Early online date13 Dec 2005
DOIs
Publication statusPublished - 2006

Keywords

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

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