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An Analog of the Paley-Wiener Theorem for Entire Functions of the Space $W _{\sigma} ^{p}, 1 < p < 2$ , and some Applications

An Analog of the Paley-Wiener Theorem for Entire Functions of the Space $W _{\sigma} ^{p}, 1 < p... We obtain an analogue of the well-known Paley-Wiener Theorem on integral representation of entire functions of exponential type at most σ, σ > 0, which belong to the space L 2(ℝ). We choose 1 < p < 2 and σ > 0 and work in L p (ℝ). We find optimal estimates of the modulus on any line parallel to ℝ, and present applications to best analytic continuation from a finite set in ℂ for entire functions of this class. The main result was announced in [7]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

An Analog of the Paley-Wiener Theorem for Entire Functions of the Space $W _{\sigma} ^{p}, 1 < p < 2$ , and some Applications

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321623
Publisher site
See Article on Publisher Site

Abstract

We obtain an analogue of the well-known Paley-Wiener Theorem on integral representation of entire functions of exponential type at most σ, σ > 0, which belong to the space L 2(ℝ). We choose 1 < p < 2 and σ > 0 and work in L p (ℝ). We find optimal estimates of the modulus on any line parallel to ℝ, and present applications to best analytic continuation from a finite set in ℂ for entire functions of this class. The main result was announced in [7].

Journal

Computational Methods and Function Theory – Springer Journals

Published: Mar 7, 2013

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