Geodesic
Analog of the Whittaker--Kotelnikov--Shannon Theorem from the Point of View of Fourier--Bessel Analysis
Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 264-272.

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In this paper, we obtain an analog of the Whittaker–Kotelnikov–Shannon theorem on the basis of the harmonic Fourier–Bessel analysis. We construct a new interpolation formula for a class of entire functions of exponential type in which generalized Bessel translations are used instead of the usual translations.
Keywords: harmonic analysis, Whittaker–Kotelnikov–Shannon (sampling) theorem, entire function of exponential type, Bessel function, Hilbert space.
Mots-clés : interpolation formula 
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S. S. Platonov. Analog of the Whittaker--Kotelnikov--Shannon Theorem from the Point of View of Fourier--Bessel Analysis. Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 264-272. http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a7/

[1] N. Viner, R. Peli, Preobrazovanie Fure v kompleksnoi oblasti, Nauka, M., 1964 | MR | Zbl

[2] V. M. Tikhomirov, “Garmoniki i splainy kak optimalnye sredstva priblizheniya i vosstanovleniya”, UMN, 50:2 (1995), 125–174 | MR | Zbl

[3] B. M. Levitan, “Razlozhenie po funktsiyam Besselya v ryady i integraly Fure”, UMN, 6:2 (1951), 102–143 | MR | Zbl

[4] S. S. Platonov, “Analogi neravenstv Bernshteina i Nikolskogo dlya odnogo klassa tselykh funktsii eksponentsialnogo tipa”, Dokl. RAN, 398:2 (2004), 168–171 | MR

[5] I. A. Kipriyanov, Singulyarnye ellipticheskie kraevye zadachi, Fizmatlit, M., 1997 | MR | Zbl

[6] K. Trimèche, Generalized Harmonic Analysis and Wavelet Packets, Gordon and Breach Sci. Publ., Amsterdam, 2001 | MR | Zbl

[7] Dzh. N. Vatson, Teoriya besselevykh funktsii, IL, M., 1949 | MR | Zbl

[8] G. Beitmen, A. Erdeii, Tablitsy integralnykh preobrazovanii, t. 2, Nauka, M., 1970 | MR | Zbl

[9] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR | Zbl

[10] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR | Zbl

[11] Ya. I. Zhitomirskii, “Zadacha Koshi dlya sistem lineinykh uravnenii v chastnykh proizvodnykh s differentsialnymi operatorami tipa Besselya”, Matem. sb., 36:2 (1955), 299–310

[12] N. I. Akhiezer, “K teorii sparennykh integralnykh uravnenii”, Uchenye zapiski Kharkovskogo gos. un-ta, 80 (1957), 5–21

[13] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR | Zbl