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A reconstruction formula for band limited functions in 
Author(s):
Isaac
Pesenson
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3593-3600.
MSC (1991):
Primary 42A65;
Secondary 42C15
Posted:
May 6, 1999
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Abstract:
It is shown that a band limited function from  can be reconstructed from irregularly sampled values as a limit of spline functions. The assumption about the sampling sequence is that it should be dense enough.
References:
- 1.
- J. J. Benedetto, Irregular sampling and frames, in Wavelets: A Tutorial in Theory and Applications (C. K. Chui, Ed.), 445-507. Academic Press, Boston, 1992. MR 93c:42030
- 2.
- H. G. Feichtinger and K. Gröchening, Theory and practice of irregular sampling, in Wavelets (J. J. Benedetto and M. W. Frazier, Eds.) pp. 305-363, CRC Press, Boca Raton, FL, 1994. MR 94i:94008
- 3.
- Yu. Lyubarskii and W. R. Madych, The recovery of irregularly sampled band limited functions via tempered splines, J. Funct. Anal. 125 (1995), 201-222. MR 96d:41013
- 4.
- W. R. Madych and S. A. Nelson, Polyharmonic cardinal splines, J. Approximation Theory 60 (1990), 141-156. MR 90j:41022
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- W. R. Madych and E. H. Potter, An estimate for multivariate interpolation, J. Approximation Theory 43 (1985), 132-139. MR 86g:65022
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- R. Paley and N. Wiener, Fourier transforms in the complex domain, in Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., Providence, 1934. MR 98a:01023
- 7.
- I. Pesenson, Sampling of Paley-Wiener functions on stratified groups, J. of Fourier Analysis and Applications 4 (3) (1998), 271-281. CMP 99:03
- 8.
- I. Pesenson, Reconstruction of Paley-Wiener functions on the Heisenberg group, Amer. Math. Soc. Transl. (2), vol. 184, 1998.
- 9.
- I, Schoenberg, Cardinal spline interpolation, CBMS, Vol. 12, SIAM, Philadelphia, 1973. MR 54:8095
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Additional Information:
Isaac
Pesenson
Affiliation:
Department of Mathematics 038-16, Temple University, Philadelphia, Pennsylvania 19122
Email:
pesenson@math.temple.edu
DOI:
10.1090/S0002-9939-99-04938-2
PII:
S 0002-9939(99)04938-2
Received by editor(s):
August 23, 1997
Received by editor(s) in revised form:
February 17, 1998
Posted:
May 6, 1999
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
1999,
American Mathematical Society
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