Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A reconstruction formula
for band limited functions in $L_2(R^d)$

Author: Isaac Pesenson
Journal: Proc. Amer. Math. Soc. 127 (1999), 3593-3600
MSC (1991): Primary 42A65; Secondary 42C15
Published electronically: May 6, 1999
MathSciNet review: 1610773
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a band limited function from $L_2(R^d)$ 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 [Enhancements On Off] (What's this?)

  • 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
  • 5. W. R. Madych and E. H. Potter, An estimate for multivariate interpolation, J. Approximation Theory 43 (1985), 132-139. MR 86g:65022
  • 6. 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42A65, 42C15

Retrieve articles in all journals with MSC (1991): 42A65, 42C15

Additional Information

Isaac Pesenson
Affiliation: Department of Mathematics 038-16, Temple University, Philadelphia, Pennsylvania 19122

Received by editor(s): August 23, 1997
Received by editor(s) in revised form: February 17, 1998
Published electronically: May 6, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society