| Title:
|
Recovery of band-limited functions on locally compact Abelian groups from irregular samples (English) |
| Author:
|
Feichtinger, H. G. |
| Author:
|
Pandey, S. S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
249-264 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
irregular sampling |
| Keyword:
|
band-limited functions |
| Keyword:
|
locally compact Abelian group |
| Keyword:
|
solid Banach spaces |
| MSC:
|
22B99 |
| MSC:
|
42C15 |
| MSC:
|
43A15 |
| MSC:
|
43A25 |
| MSC:
|
47B38 |
| MSC:
|
62D05 |
| MSC:
|
94A12 |
| MSC:
|
94A20 |
| idZBL:
|
Zbl 1021.43001 |
| idMR:
|
MR1983449 |
| . |
| Date available:
|
2009-09-24T11:01:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127797 |
| . |
| Reference:
|
[1] A. Faridani: A generalized sampling theorem for locally compact Abelian groups.Mathh. Comp. 63 (1994), 307–327. Zbl 0808.65144, MR 1240658, 10.1090/S0025-5718-1994-1240658-6 |
| Reference:
|
[2] H. G. Feichtinger: Gewichtsfunktionen auf lokalkompakten Gruppen, Sitzgsber.Österr. Akad. Wiss. 188 (1979), 451–471. MR 0599884 |
| Reference:
|
[3] H. G. Feichtinger: 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. MR 0751019 |
| Reference:
|
[4] H. G. Feichtinger: Characterization of minimal homogeneous Banach spaces.Proc. Amer. Math. Soc. 81 (1981), 55–61. Zbl 0465.43002, MR 0589135, 10.1090/S0002-9939-1981-0589135-9 |
| Reference:
|
[5] H. G. Feichtinger: Generalized amalgams, with applications to Fourier transform.Canad. J. Math. XLII (1990), 395–409. Zbl 0733.46014, MR 1062738 |
| Reference:
|
[6] H. G. Feichtinger: 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. MR 1152342 |
| Reference:
|
[7] H. G. Feichtinger and K. Gröchenig: Irregular sampling theorems and series expansions of band-limited functions.J. Math. Anal. Appl. 167 (1992), 530–556. MR 1168605, 10.1016/0022-247X(92)90223-Z |
| Reference:
|
[8] H. G. Feichtinger and K. Gröchenig: Error analysis in regular and irregular sampling theory.Appl. Anal. 50 (1993), 167–189. MR 1278324, 10.1080/00036819308840192 |
| Reference:
|
[9] H. G. Feichtinger and T. Werther: Improved locality for irregular sampling algorithms.In: Proc. ICASSP 1999, IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Istanbul, Turkey, June 1999. |
| Reference:
|
[10] H. G. Feichtinger and S. S. Pandey: Error estimates for irregular sampling of band-limited distribution on a locally compact Abelian group.J. Math. Anal. Appl. (2003) (to appear). MR 1974032 |
| Reference:
|
[11] C. Heil: 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. |
| Reference:
|
[12] I. Kluvánek: Sampling theorem in abstract harmonic analysis.Mat. Časopis Slov. Akad. Vied 15 (1969), 43–48. |
| Reference:
|
[13] H. Reiter and J. Stegeman: Classical Harmonic Analysis and Locally Compact Groups, 2nd Ed., London Mathematical Society Monographs. New Series. 22.Clarendon Press, Oxford, 2000. MR 1802924 |
| Reference:
|
[14] T. Werther: Reconstruction from irregular samples with improved locality.Master Thesis, Vienna, 1999. |
| . |
