A characterization of Lévy probability distribution functions on Euclidean spaces

A Characterization of Euclidean Spaces

The purpose of this paper is to give an elementary proof of the fact that a Banach space in which there exist projection transformations of norm one on every two-dimensional linear subspace is a euclidean space. S. Kakutani [ l ] has pointed out that a modification of a proof due to Blaschke [2] will prove this theorem. F. Bohnenblust has been able to establish this theorem for the complex case...

A Characterization of Locally Euclidean Spaces

On the Concavity of Multivariate Probability Distribution Functions on the Concavity of Multivariate Probability Distribution Functions

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

On the Distribution of Natural Probability Functions

Strictly positive definite functions on spheres in Euclidean spaces

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...