Multi-domain spectral approach for the Hilbert transform on the real line
Numerical Analysis
2021-01-08 v1 Numerical Analysis
Pattern Formation and Solitons
Abstract
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of these and other types of functions are discussed. As an application solitons to generalized Benjamin-Ono equations are constructed.
Cite
@article{arxiv.2101.02473,
title = {Multi-domain spectral approach for the Hilbert transform on the real line},
author = {C. Klein and J. Riton and N. Stoilov},
journal= {arXiv preprint arXiv:2101.02473},
year = {2021}
}