Temat: convex hull - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

Tytuł:: Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
Autorzy:: Klee, Victor
Veselý, Libor
Zanco, Clemente
Powiązania:: https://bibliotekanauki.pl/articles/1287312.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: normed linear space
reflexive
convex body
smooth
rotund
strictly convex
vector sum
convex hull
stability
Opis:: For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class of all smooth bodies in X is stable with respect to both ∓ and γ̅. In our paper it is shown that when X is separable, these stability properties of rotundity (resp. smoothness) are actually equivalent to the reflexivity of X. The characterizations remain valid for each nonseparable X that contains a rotund (resp. smooth) body.
Źródło:: Studia Mathematica; 1996, 120, 3; 191-204
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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