English

Integral representation of functions on the circle

Classical Analysis and ODEs 2024-11-05 v5 Metric Geometry

Abstract

We give a complete characterization of all real-valued functions on the unit circle S1S^1 that can be represented by integrating the spherical distance on S1S^1 with respect to a signed measure or a probability measure.

Keywords

Cite

@article{arxiv.2304.08358,
  title  = {Integral representation of functions on the circle},
  author = {Giuliano Basso},
  journal= {arXiv preprint arXiv:2304.08358},
  year   = {2024}
}

Comments

To appear in Real Analysis Exchange

R2 v1 2026-06-28T10:08:31.196Z