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Sampling and Local Deconvolution

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Harmonic Analysis, Signal Processing, and Complexity

Part of the book series: Progress in Mathematics ((PM,volume 238))

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Abstract

In a series of papers starting in the late 1970s, Carlos Berenstein and collaborators explored various aspects of the problem of recovering a function locally from its convolutions with compactly supported distributions. These problems have variously been referred to as multisensor deconvolution problems, analytic and polynomial Bezout problems, and local Pompeiu problems. The focus of Carlos’ work in this area has been to find explicit and computable solutions. The purpose of this paper is to present a point of view on a small subclass of these problems in which some classical techniques from the theory of sampling and interpolation in Paley-Wiener spaces of entire functions can shed some light on their explicit solution.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA

    David F. Walnut

Authors
  1. David F. Walnut
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, I-20133, Milano, Italy

    Irene Sabadini

  2. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA

    Daniele C. Struppa  & David F. Walnut  & 

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© 2005 Birkhäuser Boston

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Walnut, D.F. (2005). Sampling and Local Deconvolution. In: Sabadini, I., Struppa, D.C., Walnut, D.F. (eds) Harmonic Analysis, Signal Processing, and Complexity. Progress in Mathematics, vol 238. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4416-4_8

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