2024 Integral Representation of Functions on the Circle
Giuliano Basso
Real Anal. Exchange 49(2): 345-354 (2024). DOI: 10.14321/realanalexch.49.2.1698890384

Abstract

We give a complete characterization of all real-valued functions on the unit circle \(S^1\) that can be represented by integrating the spherical distance on \(S^1\) with respect to a signed measure or a probability measure.

Citation

Download Citation

Giuliano Basso. "Integral Representation of Functions on the Circle." Real Anal. Exchange 49 (2) 345 - 354, 2024. https://doi.org/10.14321/realanalexch.49.2.1698890384

Information

Published: 2024
First available in Project Euclid: 13 April 2024

Digital Object Identifier: 10.14321/realanalexch.49.2.1698890384

Subjects:
Primary: 45B05
Secondary: 26A42 , 58C05

Keywords: functions on the circle , integral representation , Stieltjes measure , Total variation , Wasserstein 1-distance

Rights: Copyright © 2024 Michigan State University Press

Vol.49 • No. 2 • 2024
Back to Top