Comptes Rendus
Mathematical Analysis/Theory of Signals
Sampling in a weighted Sobolev space
Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 941-944.

We show that functions f in some weighted Sobolev space are completely determined by time-frequency samples {f(tn)}nZ{fˆ(λk)}kZ along appropriate slowly increasing sequences {tn}nZ and {λn}nZ tending to ±∞ as n±.

Nous démontrons que toute fonction f dans un certain espace de Sobolev avec poids est complètement determinée par un échantillon {f(tn)}nZ{fˆ(λk)}kZ sur des convenables suites croissantes {tn}nZ et {λn}nZ, tendant vers ±∞ lentement, quand n±.

Published online:
DOI: 10.1016/j.crma.2012.10.028

Nestor G. Acala 1; Noli N. Reyes 1

1 University of the Philippines – Diliman, Institute of Mathematics, Quezon City, 1101, Philippines
     author = {Nestor G. Acala and Noli N. Reyes},
     title = {Sampling in a weighted {Sobolev} space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {941--944},
     publisher = {Elsevier},
     volume = {350},
     number = {21-22},
     year = {2012},
     doi = {10.1016/j.crma.2012.10.028},
     language = {en},
AU  - Nestor G. Acala
AU  - Noli N. Reyes
TI  - Sampling in a weighted Sobolev space
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 941
EP  - 944
VL  - 350
IS  - 21-22
PB  - Elsevier
DO  - 10.1016/j.crma.2012.10.028
LA  - en
ID  - CRMATH_2012__350_21-22_941_0
ER  - 
%0 Journal Article
%A Nestor G. Acala
%A Noli N. Reyes
%T Sampling in a weighted Sobolev space
%J Comptes Rendus. Mathématique
%D 2012
%P 941-944
%V 350
%N 21-22
%I Elsevier
%R 10.1016/j.crma.2012.10.028
%G en
%F CRMATH_2012__350_21-22_941_0
Nestor G. Acala; Noli N. Reyes. Sampling in a weighted Sobolev space. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 941-944. doi : 10.1016/j.crma.2012.10.028.

[1] A. Aldroubi; K. Gröchenig Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., Volume 43 (2001), pp. 585-620

[2] P.L. Butzer; P.J.S.G. Ferreira; J.R. Higgins; S. Saitoh; G. Schmeisser; R.L. Stens Interpolation and sampling: E.T. Whittaker, K. Ogura and their followers, J. Fourier Anal. Appl., Volume 17 (2010), pp. 320-354

[3] D.L. Donoho; P.B. Stark Uncertainty principles and signal recovery, SIAM J. Appl. Math., Volume 49 (1990), pp. 906-931

[4] H.G. Feichtinger; K. Gröchenig Theory and practice of irregular sampling, Wavelets: Mathematics and Applications, Stud. Adv. Math., CRC, Boca Raton, 1994, pp. 305-363

[5] K. Gröchenig Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type, Math. Comp., Volume 68 (1999), pp. 749-765

[6] V. Havin; B. Jöricke The Uncertainty Principle in Harmonic Analysis, Springer-Verlag, Berlin, 1994

[7] Y. Meyer Ondelettes et Opérateurs, Hermann, Paris, 1990

[8] E. Talvila Rapidly growing Fourier integrals, Amer. Math. Month., Volume 108 (2001), pp. 636-641

[9] W.J. Walker Zeros of the Fourier transform of a distribution, J. Math. Anal. Appl., Volume 154 (1989), pp. 77-91

Cited by Sources:

Comments - Policy