Recovery of band-limited functions on locally compact Abelian groups from irregular samples

H. G. Feichtinger; S. S. Pandey

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 2, page 249-264
  • ISSN: 0011-4642

Abstract

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Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.

How to cite

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Feichtinger, H. G., and Pandey, S. S.. "Recovery of band-limited functions on locally compact Abelian groups from irregular samples." Czechoslovak Mathematical Journal 53.2 (2003): 249-264. <http://eudml.org/doc/30774>.

@article{Feichtinger2003,
abstract = {Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group $G$. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.},
author = {Feichtinger, H. G., Pandey, S. S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {irregular sampling; band-limited functions; locally compact Abelian group; solid Banach spaces; irregular sampling; band-limited functions; locally compact Abelian group; solid Banach spaces},
language = {eng},
number = {2},
pages = {249-264},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Recovery of band-limited functions on locally compact Abelian groups from irregular samples},
url = {http://eudml.org/doc/30774},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Feichtinger, H. G.
AU - Pandey, S. S.
TI - Recovery of band-limited functions on locally compact Abelian groups from irregular samples
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 249
EP - 264
AB - Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group $G$. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.
LA - eng
KW - irregular sampling; band-limited functions; locally compact Abelian group; solid Banach spaces; irregular sampling; band-limited functions; locally compact Abelian group; solid Banach spaces
UR - http://eudml.org/doc/30774
ER -

References

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  1. 10.1090/S0025-5718-1994-1240658-6, Mathh. Comp. 63 (1994), 307–327. (1994) Zbl0808.65144MR1240658DOI10.1090/S0025-5718-1994-1240658-6
  2. Gewichtsfunktionen auf lokalkompakten Gruppen, Sitzgsber, Österr. Akad. Wiss. 188 (1979), 451–471. (1979) MR0599884
  3. Banach convolution algebras of Wiener type, In: Proc. Conf. on Functions, Series, Operators, Budapest 1980, Colloq. Math. Soc. János Bolyai Vol. 35, North-Holland, Amsterdam, 1983, pp. 509–524. (1983) MR0751019
  4. 10.1090/S0002-9939-1981-0589135-9, Proc. Amer. Math. Soc. 81 (1981), 55–61. (1981) Zbl0465.43002MR0589135DOI10.1090/S0002-9939-1981-0589135-9
  5. Generalized amalgams, with applications to Fourier transform, Canad. J. Math. XLII (1990), 395–409. (1990) Zbl0733.46014MR1062738
  6. New results on regular and irregular sampling based on Wiener amalgams, In: Proc. Conf. Function spaces, Vol.  136 of Lect. Notes in Math., K. Jarosz (ed.), M. Dekker, 1990, 1991, pp. 107–122. (1990, 1991) MR1152342
  7. 10.1016/0022-247X(92)90223-Z, J. Math. Anal. Appl. 167 (1992), 530–556. (1992) MR1168605DOI10.1016/0022-247X(92)90223-Z
  8. 10.1080/00036819308840192, Appl. Anal. 50 (1993), 167–189. (1993) MR1278324DOI10.1080/00036819308840192
  9. Improved locality for irregular sampling algorithms, In: Proc. ICASSP  1999, IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Istanbul, Turkey, June 1999. 
  10. Error estimates for irregular sampling of band-limited distribution on a locally compact Abelian group, J. Math. Anal. Appl. (2003) (to appear). (ARRAY(0x8baa228)) MR1974032
  11. An introduction to weighted Wiener amalgams, In: Proc. Int. Conf. on Wavelets and their Applications (Chennai, January 2002), R. Ramakrishnan and S. Thangavelu (eds.), Allied Publishers, New Delhi. 
  12. Sampling theorem in abstract harmonic analysis, Mat. Časopis Slov. Akad. Vied 15 (1969), 43–48. (1969) 
  13. Classical Harmonic Analysis and Locally Compact Groups, 2nd Ed., London Mathematical Society Monographs. New Series. 22, Clarendon Press, Oxford, 2000. (2000) MR1802924
  14. Reconstruction from irregular samples with improved locality, Master Thesis, Vienna, 1999. (1999) 

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