An estimate of the code length of signals with a finite spectrum in connection with sound-recording problems
Izvestiya. Mathematics, Tome 8 (1974) no. 4, pp. 867-894
Cet article a éte moissonné depuis la source Math-Net.Ru
In the article an estimate is given of the entropy of the Bernstein class $B_\sigma$. This class consists, by definition, of the real-valued functions of a single real variable that are bounded in absolute value on the real line by unity and such that the supports of their Fourier transforms are contained in the interval $[-\sigma,\sigma]$. The meaning of the estimates will be discussed in connection with sound-recording problems.
@article{IM2_1974_8_4_a4,
author = {V. I. Buslaev and A. G. Vitushkin},
title = {An estimate of the code length of signals with a~finite spectrum in connection with sound-recording problems},
journal = {Izvestiya. Mathematics},
pages = {867--894},
year = {1974},
volume = {8},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a4/}
}
TY - JOUR AU - V. I. Buslaev AU - A. G. Vitushkin TI - An estimate of the code length of signals with a finite spectrum in connection with sound-recording problems JO - Izvestiya. Mathematics PY - 1974 SP - 867 EP - 894 VL - 8 IS - 4 UR - http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a4/ LA - en ID - IM2_1974_8_4_a4 ER -
V. I. Buslaev; A. G. Vitushkin. An estimate of the code length of signals with a finite spectrum in connection with sound-recording problems. Izvestiya. Mathematics, Tome 8 (1974) no. 4, pp. 867-894. http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a4/
[1] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya, $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, Uspekhi matem. nauk, 14:2 (1959), 3–86 | MR
[2] Levin B. Ya., Tselye funktsii, kurs lektsii, In-t mekhaniki MGU, M., 1971
[3] Bernshtein S. N., Sobr. soch., t. 2, AN SSSR, M., 1952, str. 443
[4] Bernshtein S. N., Sobr. soch., t. 1, AN SSSR, M., 1952, str. 21