Work

Complete monotonicity of log-functions

Year: 2025

Type: article

Abstract: In this article we investigate the property of complete monotonicity within a special family $$\mathcal {F}_s$$ F s of functions in s variables involving logarithms. The main result of this work provides a linear isomorphism between $$\mathcal {F}_s$$ F s and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in $$\mathcal {F}_s$$ F s is semi-algebraic. This gives a finite time algorithm to decide whether a function in $$\mathcal {F}_s$$ F s is completely monotone.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-025-01136-9

Authors: Rourou Ma, Julian Weigert

Institutions: University of Science and Technology of China, Max Planck Institute for Physics, Max Planck Institute for Mathematics in the Sciences, Leipzig University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Deutsche Forschungsgemeinschaft, University of Science and Technology of China, Max-Planck-Institut für Mathematik in den Naturwissenschaften, HORIZON EUROPE European Research Council