- Tytuł:
- Metric entropy of convex hulls in Hilbert spaces
- Autorzy:
-
Li, Wenbo V.
Linde, Werner - Powiązania:
- https://bibliotekanauki.pl/articles/1206124.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
metric entropy
convex hull
majorizing measure
Gaussian process - Opis:
- Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), $T={t_1,t_2,...}$, $||t_j||≤a_j$, by functions of the $a_j$'s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences $(a_j)_{j=1}^∞$.
- Źródło:
-
Studia Mathematica; 2000, 139, 1; 29-45
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł