Add to ORKGThe volume of the unit ball of the Lebesgue sequence space `mp is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm `nq (` m p), 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.
Abstract. In the family of unit balls with constant volume we look at the ones whose algebraic repre...
This paper collects together a miscellany of results originally motivated by the analysis of the gen...
We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an a...
This thesis studies the volume of the unit ball of finite-dimensional Lorentz sequence spaces p,q n ...
Abstract. In this short paper, we compute the volume of n-dimensional balls in Rn. The computations ...
In this article, we prove that from any sequence of balls whose associated limsup set has full µ-mea...
We characterize lacunary series in mixed norm spaces on the unit ball B n in C n and on the unit pol...
summary:This article provided some sufficient or necessary conditions for a class of integral operat...
Volume estimates of metric balls in manifolds find diverse applications in information and coding th...
International audienceBalls and spheres are amongst the simplest 3D modeling primitives, and computi...
Geometry in very high dimensions is full of surprises, many of the properties of high dimensional ge...
Abstract—This paper presents a non-asymptotic study of the minimax estimation of high-dimensional me...
Since Stein's original proposal in 1962, a series of papers have constructed confidence regions of s...
We study a family of polytopes and their duals, that appear in various optimization problems as the ...
AbstractUsing techniques of a geometrical nature, the following result is proved: denoting by Iqp(M)...
Abstract. In the family of unit balls with constant volume we look at the ones whose algebraic repre...
This paper collects together a miscellany of results originally motivated by the analysis of the gen...
We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an a...
This thesis studies the volume of the unit ball of finite-dimensional Lorentz sequence spaces p,q n ...
Abstract. In this short paper, we compute the volume of n-dimensional balls in Rn. The computations ...
In this article, we prove that from any sequence of balls whose associated limsup set has full µ-mea...
We characterize lacunary series in mixed norm spaces on the unit ball B n in C n and on the unit pol...
summary:This article provided some sufficient or necessary conditions for a class of integral operat...
Volume estimates of metric balls in manifolds find diverse applications in information and coding th...
International audienceBalls and spheres are amongst the simplest 3D modeling primitives, and computi...
Geometry in very high dimensions is full of surprises, many of the properties of high dimensional ge...
Abstract—This paper presents a non-asymptotic study of the minimax estimation of high-dimensional me...
Since Stein's original proposal in 1962, a series of papers have constructed confidence regions of s...
We study a family of polytopes and their duals, that appear in various optimization problems as the ...
AbstractUsing techniques of a geometrical nature, the following result is proved: denoting by Iqp(M)...
Abstract. In the family of unit balls with constant volume we look at the ones whose algebraic repre...
This paper collects together a miscellany of results originally motivated by the analysis of the gen...
We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an a...