| 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:
|
http://hdl.handle.net/10338.dmlcz/141606 |
| . |
| 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 |
| Reference:
|
[2] Higgins J.R.: Five short stories about the cardinal series.Bull. Amer. Math. Soc. 12 (1985), 45–89. Zbl 0562.42002, MR 0766960, 10.1090/S0273-0979-1985-15293-0 |
| 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 theorem.in 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 |
| . |
