Sampling in the functional hilbert space induced by a hilbert space valued kernel

Applicable Analysis

Volumn 82, Issue 12, 2003, Pages 1145-1158

  García, Antonio G ^a   Portal, Alberto ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

AMS Subject Classifications: 94A20; 44A05; 46E22; Biorthonormal Riesz bases; Reproducing kernel Hilbert spaces; Sampling formulas

Indexed keywords

EID: 24244434156     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/0003681031000063748     Document Type: Article

References (15)

1. Aronszajn, N., 1950. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68: 337–404.
2. García, A.G., 1997. The Paley-Wiener-Levinson theorem revisited. Int. J. Math. Math. Sci., 20: 229–234.
3. García, A.G., 2000. Orthogonal sampling formulas: a unified approach. SIAM Review, 42: 499–512.
4. García, A.G., and Hernández-Medina, M.A., 2001. The discrete Kramer sampling theorem and indeterminate moment problems. J. Comp. Appl. Math., 134: 13–22.
5. García, A.G., and Szafraniec, F.H., 2002. A Converse of the Kramer sampling theorem. Sampling Theory in Signal and Image Processing, 1: 53–61.
6. Higgins J.R., 1996 Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford University Press Oxford
7. Higgins J.R., 2001 A sampling principle associated with Saitoh’s fundamental theory of linear transformations In: S. Saitoh et al. (Eds.) Analytic Extension Formulas and Their Applications pp. 73–86 Kluwer Academic Publishers Dordrecht The Netherlands
8. Higgins J.R., Stens R.L., Eds. 1999 Sampling Theory in Fourier and Signal Analysis: Advanced Topics pp. 56–77 Oxford University Press Oxford
9. Nashed, M.Z., and Walter, G.G., 1991. General sampling theorems in reproducing kernel Hilbert spaces. Math. Control Signals Sys., 4: 373–412.
10. Paley R.E.A.C., Wiener N., 1934 19 Fourier Transforms in the Complex Domain AMS Colloq. Publ. AMS, New York
11. Saitoh S., 1997 Integral Transforms Reproducing Kernels and Their Applications. Longman Essex, England
12. Szafraniex, F.H., 2000. The reproducing kernel Hilbert space and its multiplication operators. Operator Th. Adv. Appl., 114: 253–263.
13. Young R.M., 1980 An Introduction of Nonharmonic Fourier Series. Academic Press New York
14. Zayed A.I., 1993 Advances in Shannon’s Sampling Theory CRC Press Boca Raton
15. Zayed A.I., Butzer P.L., 2001 Langrange interpolation and sampling theorems In: F. Marvasti (Ed.) Nonuniform Sampling: Theory and Practice pp. 123–168 Kluwer Academic New York