Geodesic
Metric entropy of convex hulls in Hilbert spaces
Studia Mathematica, Tome 139 (2000) no. 1, pp. 29-45

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $(a_j)_{j=1}^∞$.
DOI : 10.4064/sm-139-1-29-45
Keywords: metric entropy, convex hull, majorizing measure, Gaussian process

Wenbo V. Li 1 ;  1

1 
@article{10_4064_sm_139_1_29_45,
     author = {Wenbo V. Li and  },
     title = {Metric entropy of convex hulls in {Hilbert} spaces},
     journal = {Studia Mathematica},
     pages = {29--45},
     publisher = {mathdoc},
     volume = {139},
     number = {1},
     year = {2000},
     doi = {10.4064/sm-139-1-29-45},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-139-1-29-45/}
}
TY  - JOUR
AU  - Wenbo V. Li
AU  -  
TI  - Metric entropy of convex hulls in Hilbert spaces
JO  - Studia Mathematica
PY  - 2000
SP  - 29
EP  - 45
VL  - 139
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-139-1-29-45/
DO  - 10.4064/sm-139-1-29-45
LA  - en
ID  - 10_4064_sm_139_1_29_45
ER  - 
%0 Journal Article
%A Wenbo V. Li
%A  
%T Metric entropy of convex hulls in Hilbert spaces
%J Studia Mathematica
%D 2000
%P 29-45
%V 139
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-139-1-29-45/
%R 10.4064/sm-139-1-29-45
%G en
%F 10_4064_sm_139_1_29_45
Wenbo V. Li;  . Metric entropy of convex hulls in Hilbert spaces. Studia Mathematica, Tome 139 (2000) no. 1, pp. 29-45. doi: 10.4064/sm-139-1-29-45

Cité par Sources :