Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems

D. V. Chudnovsky (), G. V. Chudnovsky () and T. Morgan ()
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D. V. Chudnovsky: Polytechnic Institute of NYU, IMAS
G. V. Chudnovsky: Polytechnic Institute of NYU, IMAS
T. Morgan: Polytechnic Institute of NYU, IMAS

A chapter in Additive Number Theory, 2010, pp 77-98 from Springer

Abstract: Summary Reconstruction of signals and their Fourier transforms lead to the theory of prolate functions, developed by Slepian and Pollack. We look at prior contributions by Szegö to these problems. We present a unified framework for solutions of Szegö like problems for signals supported by an arbitrary union of intervals, using the techniques of Garnier isomonodromy equations. New classes of completely integrable equations and Darboux–Backlund transformations that arise from this framework are similar to the problems encountered in transcendental number theory. A particular example for the Hilbert matrix is studied in detail.

Keywords: Hilbert matrix; Hankel matrices; Padé approximations (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-68361-4_5

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DOI: 10.1007/978-0-387-68361-4_5

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