Generalized convexity of spectral functions on Euclidean Jordan algebras

Juyoung Jeong

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arXiv · 2606.25507

Generalized convexity of spectral functions on Euclidean Jordan algebras

Juyoung Jeong

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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.

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Juyoung Jeong. 2026-06-24. Generalized convexity of spectral functions on Euclidean Jordan algebras. https://arxiv.org/abs/2606.25507

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