An Infinite Dimensional Version of the Kostant Convexity Theorem

On the Nonlinear Convexity Theorem of Kostant

A classical result of Schur and Horn [Sc, Ho] states that the set of diagonal elements of all n x n Hermitian matrices with fixed eigenvalues is a convex set in IRn. Kostant [Kt] has generalized this result to the case of any semisimple Lie group. This is often referred to as the linear convexity theorem of Kostant: picking up the diagonal of a Hermitian matrix is a linear operation. This resul...

An Infinite Dimensional Version of a Theorem of Bernstein

1. Introduction. Let (R") is the algebra Q1(Rn) of all real-valued functions of class C1. In other words, for every fEG1(Rn) there is a sequence {pn} of polynomials such that pn—*/ uniformly o...

An Infinite Dimensional Convolution Theorem

An Infinite Dimensional Convolution Theorem

An Infinite Dimensional Convolution Theorem