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This article is cited in 1 scientific paper (total in 1 paper)
Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric
A. A. Panov Moscow Mining Institute
Abstract:
The number $K_{p,q}$, i.e., the number of $(p,q)$ corridors of closed domains which are convex in the vertical direction, consist of elementary squares of the integral lattice, are situated within a rectangle of the size $q\times p$, and completely cover the side of length $p$ of this rectangle under projection is computed. The asymptotic $(K_{p,q}/q^2)^{1/p}\to\lambda$, as $p,q\to\infty$, where $\lambda=0,\!3644255\dots$ is the maximum root of the equation $_1F_1(-1/2-1/(16\lambda),1/2,1/(4\lambda))=0$, $_1F_1$ being the confluence hypergeometric function, is established. These results allow us to compute the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric.
Received: 06.03.1974
Citation:
A. A. Panov, “Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric”, Mat. Zametki, 21:1 (1977), 39–50; Math. Notes, 21:1 (1977), 22–28
Linking options:
https://www.mathnet.ru/eng/mzm7927 https://www.mathnet.ru/eng/mzm/v21/i1/p39
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Abstract page: | 183 | Full-text PDF : | 76 | First page: | 1 |
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