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This article is cited in 1 scientific paper (total in 1 paper)
Linear algorithms of affine synthesis in the Lebesgue space $L^1[0,1]$
P. A. Terekhin Saratov State University named after N. G. Chernyshevsky
Abstract:
We prove that there are no linear algorithms of affine synthesis
for affine systems in the Lebesgue space $L^1[0,1]$ with respect to the
model space $\ell^1$, although the corresponding affine
synthesis problem has a positive solution under the most general
assumptions. At the same time, by imposing additional conditions
on the generating function of the affine system, we can give an explicit
linear algorithm of affine synthesis in the Lebesgue space when the
model space is that of the coefficients of the system.
This linear algorithm generalizes the Fourier–Haar expansion
into orthogonal series.
Keywords:
affine system, affine synthesis, frames in Banach spaces, representation system, Fourier–Haar series, primary space.
Received: 05.08.2008
Citation:
P. A. Terekhin, “Linear algorithms of affine synthesis in the Lebesgue space $L^1[0,1]$”, Izv. RAN. Ser. Mat., 74:5 (2010), 115–144; Izv. Math., 74:5 (2010), 993–1022
Linking options:
https://www.mathnet.ru/eng/im3562https://doi.org/10.1070/IM2010v074n05ABEH002513 https://www.mathnet.ru/eng/im/v74/i5/p115
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Abstract page: | 634 | Russian version PDF: | 269 | English version PDF: | 32 | References: | 54 | First page: | 9 |
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