Sampling in a Hilbert space

Proceedings of the American Mathematical Society

Volumn 124, Issue 12, 1996, Pages 3767-3776

  Zayed, Ahmed I ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Frames and frame operators; Interpolation and approximation in a Hilbert space; Shannon's sampling theorem

Indexed keywords

EID: 21444458291     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-96-03526-5     Document Type: Article

References (15)

1. J. Benedetto, Frame decompositions, sampling and uncertainty principle inequalities, Wavelets: Mathematics and Applications, Editors, J. Benedetto and M. Frazier, CRC Press, Boca Raton, FL (1994), pp. 247-304. MR 94i:94005
2. _, Irregular sampling and frames, Wavelet-A Tutorial, Editor C. Chui, Academic Press (1991), pp. 1-63. MR 93c:42030
3. J. Benedetto and W. Heller, Irregular sampling and the theory of frames I, Note di Matematica, Vol. X, Suppl. 1 (1990), pp. 103-125. MR 94e:9400G
4. F. Beutler, Error-free recovery of signals from irregularly spaced samples, SIAM Rev. 8 (1966), pp. 328-335. MR 34:5568
5. _, Sampling theorems and bases in a Hilbert space, Information and Control, 4 (1961), pp. 97-117. MR 26:4832
6. R. Boas, Entire Functions, Academic Press, New York (1954). MR 16:914f
7. C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev., Vol. 31 (1989), pp. 628-666. MR 91c:42032
8. H. Kramer, A generalized sampling theorem, J. Math. Phys., 63 (1959/60), pp. 68-72. MR 21:2550
9. N. Levinson, Gap and Density Theorem, Amer. Math. Soc. Colloq. Pubis., Ser., Vol. 26, Amer. Math. Soc., Providence, RI (1940). MR 2:180d
10. J. Mikusinski, The Bochner integral, Birkäuser, Basel (1978). MR 58:11296
11. R. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publs., Ser., Vol. 19, Amer. Math. Soc., Providence, RI (1934). MR 31:5038
12. C. E. Shannon, A mathematical theory of communication, Bell System Tech. Report Journal, Vol. 27 (1948), pp. 379-423. MR 10:133e
13. K. Yao, Applications of reproducing kernel Hilbert space of band-limited signal models, Information and Control, Vol. 11 (1967), pp. 429-444.
14. A. I. Zayed, Advances in Shannon's sampling theory, CRC Press, Boca Raton, FL (1993). MR 95f:94008
15. _, A new role of Green's function in interpolation and sampling theory, J. Math. Anal. Appl., 175 (1993), pp. 272-238. MR 94d:41001