Work

Polynomial valuations on convex functions and their maximal extensions

Year: 2025

Type: article

Abstract: A unified framework to investigate polynomial valuations on various spaces of convex functions is introduced. It is shown that these different spaces of valuations can be essentially studied as one single class of valuations defined on a particular cone of convex functions. The corresponding extension problem reduces to a single geometric obstruction on the support of these valuations. As an application, explicit integral representations for a subclass of these valuations are established.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111253

Authors: Jonas Knoerr, Jacopo Ulivelli

Institution: TU Wien

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Austrian Science Fund, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Technische Universität Wien Bibliothek