On the supremum of a quotient of power sums

Stefan Gerhold; Friedrich Hubalek

doi:10.1186/s13660-026-03459-y

March 19, 2026Journal of Inequalities and ApplicationsOpen Access

On the supremum of a quotient of power sums

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Key Points

The research aims to define a function for real vectors based on power sums and explore its supremum's growth relative to dimension.
Defined a homogeneous quotient involving power sums for two real vectors.
Analyzed the asymptotic behavior of the supremum in relation to vector dimensions.
Established conditions for polynomial positivity constraints in a set of real matrices.
Demonstrated that the supremum grows asymptotically in a linear manner with respect to dimension.
Identified specific conditions under which real matrices satisfy polynomial positivity constraints.
Applied the findings to mathematical finance, particularly in price impact models.

Implication

Analysis shows linear growth of the supremum in dimension, indicating polynomial positivity constraints in matrices.

Abstract

We define a function of two real vectors by a certain homogeneous quotient involving power sums, and show that its supremum grows asymptotically linearly w.r.t. the dimension. From this, we deduce a condition under which a parametric set of real matrices satisfies a set of polynomial positivity constraints. This characterization finds an application in mathematical finance, in a recent study on price impact models.

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Cite This Study

Gerhold et al. (2026) studied this question.

synapsesocial.com/papers/69be36766e48c4981c67570c https://doi.org/10.1186/s13660-026-03459-y

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On the supremum of a quotient of power sums

Key Points

Implication

Abstract

Discussion

Cite This Study

On the supremum of a quotient of power sums

Key Points

Implication

Abstract

Discussion

Cite This Study

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