On the greatest zero of an orthogonal polynomial
Journal of Approximation Theory
Polynomial analogues of prolate spheroidal wave functions and uncertainty
SIAM Journal on Mathematical Analysis
Orthogonal polynomials: their growth relative to their sums
Journal of Approximation Theory
Wavelets based on orthogonal polynomials
Mathematics of Computation
Spatiospectral Concentration on a Sphere
SIAM Review
On a filter for exponentially localized kernels based on Jacobi polynomials
Journal of Approximation Theory
Szego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials (M. B. Porter Lectures)
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The aim of this article is to present a time-frequency theory for orthogonal polynomials on the interval [-1,1] that runs parallel to the time-frequency analysis of bandlimited functions developed by Landau, Pollak and Slepian. For this purpose, the spectral decomposition of a particular compact time-frequency operator is studied. This decomposition and its eigenvalues are closely related to the theory of orthogonal polynomials. Results from both theories, the theory of orthogonal polynomials and the Landau-Pollak-Slepian theory, can be used to prove localization and approximation properties of the corresponding eigenfunctions. Finally, an uncertainty principle is proven that reflects the limitation of coupled time and frequency locatability.