Volumes of unit balls of mixed sequence spaces
Functional Analysis
2015-06-26 v2
Abstract
The volume of the unit ball of the Lebesgue sequence space is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm , whose special cases are nowadays popular in machine learning under the name of group lasso. We consider the real as well as the complex case. The result is given by a closed formula involving the gamma function, only slightly more complicated than the one of Dirichlet. We close by an overview of open problems.
Keywords
Cite
@article{arxiv.1505.05867,
title = {Volumes of unit balls of mixed sequence spaces},
author = {Henning Kempka and Jan Vybíral},
journal= {arXiv preprint arXiv:1505.05867},
year = {2015}
}