A multidimensional distribution sampling theorem

Francisco Javier González Vieli

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 3, page 341-347
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Vieli, Francisco Javier González. "A multidimensional distribution sampling theorem." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 341-347. <http://eudml.org/doc/246582>.

@article{Vieli2011,
abstract = {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.},
author = {Vieli, Francisco Javier González},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sampling theorem; distributions; Fourier transform; sampling theorem; distribution; Fourier transform},
language = {eng},
number = {3},
pages = {341-347},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A multidimensional distribution sampling theorem},
url = {http://eudml.org/doc/246582},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Vieli, Francisco Javier González
TI - A multidimensional distribution sampling theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 3
SP - 341
EP - 347
AB - 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.
LA - eng
KW - sampling theorem; distributions; Fourier transform; sampling theorem; distribution; Fourier transform
UR - http://eudml.org/doc/246582
ER -

References

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  1. González Vieli F.J., 10.1007/s000130050506, Archiv Math. 75 (2000), 290–298. MR1786175DOI10.1007/s000130050506
  2. Higgins J.R., 10.1090/S0273-0979-1985-15293-0, Bull. Amer. Math. Soc. 12 (1985), 45–89. Zbl0562.42002MR0766960DOI10.1090/S0273-0979-1985-15293-0
  3. Liu Y., 10.1137/S0036141094266930, SIAM J. Math. Anal. 27 (1996), 1153–1157. Zbl0857.40005MR1393431DOI10.1137/S0036141094266930
  4. Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971. Zbl0232.42007MR0304972
  5. Walter G., 10.1137/0519084, SIAM J. Math. Anal. 19 (1988), 1198–1203. MR0957679DOI10.1137/0519084
  6. Walter G., Abel summability for a distribution sampling theorem, in Generalized Functions, Convergence Structures, and their Applications (B. Stanković e.a. editors), Plenum Press, New York, 1988, pp. 349–357. Zbl0736.40006MR0975746
  7. Watson G.N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1922. Zbl0849.33001MR1349110

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