A note on the periodic Hilbert Transform on a strip
Analysis of PDEs
2024-11-04 v1 Classical Analysis and ODEs
Number Theory
Abstract
In this note we prove a conjecture by Constantin--Strauss--V\u{a}rv\u{a}ruc\u{a} related to the finite depth water wave problem, tightening their results. The proof uses identities related to Jacobi Theta functions. We also discuss potential implications of the improvement.
Keywords
Cite
@article{arxiv.2411.00280,
title = {A note on the periodic Hilbert Transform on a strip},
author = {Javier Gómez-Serrano and Sieon Kim},
journal= {arXiv preprint arXiv:2411.00280},
year = {2024}
}
Comments
5 pages, 1 figure