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arXiv · 2411.00280

A note on the periodic Hilbert Transform on a strip

Javier Gómez-Serrano·Sieon Kim
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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.

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Javier Gómez-Serrano, Sieon Kim. 2024-11-01. A note on the periodic Hilbert Transform on a strip. https://arxiv.org/abs/2411.00280

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