Eigenvalues of periodic Sturm-Liouville problems by the Shannon-Whittaker sampling theorem

DOI10.1090/S0025-5718-99-01053-4zbMath0920.34068OpenAlexW2031069562MaRDI QIDQ4240579

Amin Boumenir

Publication date: 28 April 1999

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01053-4

zbMATH Keywords

interpolationeigenvalue problemperiodic Sturm-Liouville problemsShannon-Whittaker sampling theorem

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Trigonometric interpolation (42A15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (15)

Sampling for the fourth-order Sturm--Liouville differential operator ⋮ Eigenvalue problems, spectral parameter power series, and modern applications ⋮ Spectral parameter power series representation for Hill's discriminant ⋮ Sampling the eigenvalues of a graph ⋮ ASYMPTOTIC ANALYSIS OF STURM-LIOUVILLE PROBLEM WITH DIRICHLET AND NONLOCAL TWO-POINT BOUNDARY CONDITIONS ⋮ Spectrum of periodic Sturm-Liouville problems involving additional transmission conditions ⋮ Truncation, amplitude, and jitter errors on \(\mathbb R\) for sampling series derivatives ⋮ Asymptotic analysis of Sturm-Liouville problem with Neumann and nonlocal two-point boundary conditions ⋮ Unnamed Item ⋮ Approximating eigenvalues of discontinuous problems by sampling theorems ⋮ A rigorous verification of a numerically computed eigenvalue ⋮ Transmutation Operators and Their Applications ⋮ An Overview of the Computation of the Eigenvalues Using Sinc-Methods ⋮ Sampling the miss-distance and transmission function ⋮ Sampling eigenvalues by Hermite revisited

Cites Work

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• Approximations via Whittaker's cardinal function
• Erratum: Eigenvalue and eigenfunction asymptotics for regular Sturm- Liouville problems
• On the spectral functions of the string
• The transmutation operator for −d²/(w(x) dx²)
• Eigenvalues of s-l systems using sampling theory
• Some Eigenfunction Expansion Formulae

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