English

The Leray transform: distinguished measures, symmetries and polygamma inequalities

Complex Variables 2025-05-28 v3

Abstract

New symmetries, norm computations and spectral information are obtained for the Leray transform on a class of unbounded hypersurfaces in C2\mathbb{C}^2. Emphasis is placed on certain distinguished measures, with results on operator norm monotonicity established by proving new polygamma inequalities. Classical techniques of Bernstein-Widder and Euler-Maclaurin play crucial roles in our analysis. Underpinning this work is a projective geometric theory of duality, which manifests here in the form of H\"older invariance.

Keywords

Cite

@article{arxiv.2401.17490,
  title  = {The Leray transform: distinguished measures, symmetries and polygamma inequalities},
  author = {Luke D. Edholm and Yonatan Shelah},
  journal= {arXiv preprint arXiv:2401.17490},
  year   = {2025}
}

Comments

30 pages, 2 figures with 10 total graphs, 4 tables. A carefully notated Mathematica notebook to help walk the reader through difficult calculations in Section 5 and the Appendix can be found on the first author's Github page: https://github.com/ledholm/Leray-measures-2024-Mathematica-nb/releases/tag/v1.0