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A general HELP inequality connected with symmetric operators

Langer, M. (2006) A general HELP inequality connected with symmetric operators. Proceedings A: Mathematical, Physical and Engineering Sciences, 462 (2066). pp. 587-606. ISSN 1364-5021

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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.