Generalized convexity of spectral functions on Euclidean Jordan algebras

Abstract

This paper investigates transfer principles for generalized convexity of spectral functions on Euclidean Jordan algebras. A spectral function is induced by the eigenvalue map and an underlying symmetric function on a symmetric subset of $\mathbb{R}^n$. We establish transfer principles for several generalized convexity notions, such as (strict/semistrict) quasiconvexity and (strict) pseudoconvexity, together with their strong variants, by showing that these properties are preserved in both directions between a spectral function and its associated symmetric function. These results extend the transfer principles for (strict) convexity and provide a unified framework for generalized convexity in the setting of Euclidean Jordan algebras.