The Leray transform: distinguished measures, symmetries and polygamma inequalities
Abstract
New symmetries, norm computations and spectral information are obtained for the Leray transform on a class of unbounded hypersurfaces in . 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