Article
Keywords:
sampling theorem; distributions; Fourier transform
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.
References:
[4] Stein E.M., Weiss G.:
Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton, N.J., 1971.
MR 0304972 |
Zbl 0232.42007
[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.
MR 0975746 |
Zbl 0736.40006
[7] Watson G.N.:
A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge, 1922.
MR 1349110 |
Zbl 0849.33001