Multi-domain spectral approach for the Hilbert transform on the real line

Christian Klein (), Julien Riton () and Nikola Stoilov ()
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Christian Klein: Université de Bourgogne-Franche-Comté
Julien Riton: Université de Bourgogne-Franche-Comté
Nikola Stoilov: Université de Bourgogne-Franche-Comté

Partial Differential Equations and Applications, 2021, vol. 2, issue 3, 1-19

Abstract: 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.

Keywords: 44A15; 65R10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00094-8

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