Numerical Determination of the Titchmarsh-Weyl m-Coefficient and Its Applications to HELP Inequalities

Numerical Determination of the Titchmarsh-Weyl m-Coefficient and Its Applications to HELP Inequalities

This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) int...

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Veröffentlicht in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1989-11, Vol.426 (1870), p.167-188
Hauptverfasser: Brown, B. M., Kirby, V. G., Pryce, J. D.
Format: Artikel
Sprache:eng
Schlagworte:
Analytical estimating
Approximation
Boundary conditions
Circles
Eigenvalues
Error rates
Exact sciences and technology
Mathematical inequalities
Mathematical integrals
Mathematics
Null set
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods
Ordinary differential equations
Sciences and techniques of general use
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Beschreibung
Zusammenfassung:This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) integral inequality.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1989.0122