Abstract:
In this paper, we calculate the mean dimension
of some subspaces of the spaces
Lp(R)
defined using equidistant shifts of a function.
As a consequence, the subspaces under consideration
turn out to be extremal in some problems
of mean square approximations of classes of convolutions
in the sense of the theory of widths.
Keywords:
sharp constants, shift spaces, mean dimension.
Citation:
O. L. Vinogradov, “Average dimension of shift spaces and their subspaces”, Mat. Zametki, 116:5 (2024), 694–706; Math. Notes, 116:5 (2024), 949–959
\Bibitem{Vin24}
\by O.~L.~Vinogradov
\paper Average dimension of shift spaces and their subspaces
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 5
\pages 694--706
\mathnet{http://mi.mathnet.ru/mzm14216}
\crossref{https://doi.org/10.4213/mzm14216}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 5
\pages 949--959
\crossref{https://doi.org/10.1134/S0001434624110075}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85218179038}
Linking options:
https://www.mathnet.ru/eng/mzm14216
https://doi.org/10.4213/mzm14216
https://www.mathnet.ru/eng/mzm/v116/i5/p694
This publication is cited in the following 1 articles:
O. L. Vinogradov, A. Yu. Ulitskaya, “Optimalnye podprostranstva dlya srednekvadratichnykh priblizhenii klassov differentsiruemykh funktsii na poluosi”, Issledovaniya po prikladnoi matematike i informatike. III, Zap. nauchn. sem. POMI, 539, POMI, SPb., 2024, 44–65
Citation in format AMSBIB
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