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

Author

Listed:
  • Christian Klein

    (Université de Bourgogne-Franche-Comté)

  • Julien Riton

    (Université de Bourgogne-Franche-Comté)

  • Nikola Stoilov

    (Université de Bourgogne-Franche-Comté)

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.

Suggested Citation

  • Christian Klein & Julien Riton & Nikola Stoilov, 2021. "Multi-domain spectral approach for the Hilbert transform on the real line," Partial Differential Equations and Applications, Springer, vol. 2(3), pages 1-19, June.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:3:d:10.1007_s42985-021-00094-8
    DOI: 10.1007/s42985-021-00094-8
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    References listed on IDEAS

    as
    1. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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