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

  • D. V. ChudnovskyEmail author
  • G. V. Chudnovsky
  • T. Morgan
Chapter

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 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • D. V. Chudnovsky
    • 1
    Email author
  • G. V. Chudnovsky
    • 1
  • T. Morgan
    • 1
  1. 1.Polytechnic Institute of NYU, IMASBrooklynUSA

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