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Title: A multidimensional distribution sampling theorem (English)
Author: Vieli, Francisco Javier González
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 52
Issue: 3
Year: 2011
Pages: 341-347
Summary lang: English
Category: math
Summary: Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions. (English)
Keyword: sampling theorem
Keyword: distributions
Keyword: Fourier transform
MSC: 42B10
MSC: 46F12
idZBL: Zbl 1250.42035
idMR: MR2843227
Date available: 2011-08-15T19:08:14Z
Last updated: 2013-10-14
Stable URL:
Reference: [1] González Vieli F.J.: Inversion de Fourier ponctuelle des distributions à support compact.Archiv Math. 75 (2000), 290–298. MR 1786175, 10.1007/s000130050506
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Reference: [3] Liu Y.: A distributional sampling theorem.SIAM J. Math. Anal. 27 (1996), 1153–1157. Zbl 0857.40005, MR 1393431, 10.1137/S0036141094266930
Reference: [4] Stein E.M., Weiss G.: Introduction to Fourier Analysis on Euclidean Spaces.Princeton University Press, Princeton, N.J., 1971. Zbl 0232.42007, MR 0304972
Reference: [5] Walter G.: Sampling band-limited functions of polynomial growth.SIAM J. Math. Anal. 19 (1988), 1198–1203. MR 0957679, 10.1137/0519084
Reference: [6] Walter G.: Abel summability for a distribution sampling Generalized Functions, Convergence Structures, and their Applications (B. Stanković e.a. editors), Plenum Press, New York, 1988, pp. 349–357. Zbl 0736.40006, MR 0975746
Reference: [7] Watson G.N.: A Treatise on the Theory of Bessel Functions.Cambridge University Press, Cambridge, 1922. Zbl 0849.33001, MR 1349110


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