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The Paley-Wiener-Levinson theorem revisited. (English) Zbl 0878.30022
Summary: In this paper a new proof of the Paley-Wiener-Levinson theorem is presented. This proof is based upon the isometry between the Paley-Wiener space and that of the square-integrable functions in \([-\pi,\pi]\), on one hand, and a Titchmarsh’s theorem which allows recovering bandlimited, entire functions from their zeros, on the other hand.

MSC:
30D10 Representations of entire functions of one complex variable by series and integrals
30D20 Entire functions of one complex variable (general theory)
41A05 Interpolation in approximation theory
42A65 Completeness of sets of functions in one variable harmonic analysis
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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