An infinite dimensional version of the Schur convexity property and applications

Claude Vallee (1) , Vicentiu Radulescu (2)

1 LMS - Laboratoire de mécanique des solides
2 Department of Mathematics

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the present paper are illustrated by several examples from mechanics or quantum mechanics, including the Sturm-Liouville problem, the Schrödinger equation, and the harmonic oscillator.

Mots clés: Schur convexity; selfadjoint operator; convex function; eigenvalue; Schrödinger equation

Domaines: Equations aux dérivées partielles [math.AP]

Claude Vallee, Vicentiu Radulescu. An infinite dimensional version of the Schur convexity property and applications. 2006. ⟨hal-00087301⟩