On sampling associated with singular Sturm-Liouville eigenvalue problems: The limit-circle case.

DOI10.1216/rmjm/1030539680zbMath1041.34078OpenAlexW1979420680MaRDI QIDQ1415029

Mahmoud H. Annaby, Paul L. Butzer

Publication date: 3 December 2003

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol32-2/CONT32-2/CONT32-2.html

zbMATH Keywords

Legendre functionssampling theorysingular Sturm-Liouville problemsof first and second kind, Bessel's functions

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Sampling theory in information and communication theory (94A20)

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On sampling theory associated with the resolvents of singular Sturm-Liouville problems ⋮ On sampling theory and basic Sturm-Liouville systems ⋮ Sampling in Paley-Wiener spaces associated with fractional integro-differential operators ⋮ Kramer-type sampling theorems associated with higher-order differential equations ⋮ \(q\)-type sampling theorems ⋮ SAMPLING AND BIRKHOFF REGULAR PROBLEMS

Cites Work

• Asymptotic formulae for eigenvalues of limit circle problems on a half line
• The continuous Legendre transform, its inverse transform, and applications
• On the inversion of integral transforms associated with Sturm-Liouville problems
• On Kramer’s Sampling Theorem Associated with General Sturm-Liouville Problems and Lagrange Interpolation
• EXPANSIONS IN LEGENDRE FUNCTIONS
• Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity, I
• Singular Second-Order Operators: The Maximal and Minimal Operators, and Selfadjoint Operators in Between
• Parametrizations of Titchmarsh's m(λ)-Functions in the Limit Circl Case
• A NOTE ON THE SELF-ADJOINT DOMAINS OF SECOND-ORDER DIFFERENTIAL EQUATIONS
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