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Inequalities and Approximations for the Finite Hilbert Transform: A Survey of Recent Results

In: Mathematical Analysis and Applications

Author

Listed:
  • Silvestru Sever Dragomir

    (Victoria University
    University of the Witwatersrand)

Abstract

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priori the accuracy.

Suggested Citation

  • Silvestru Sever Dragomir, 2019. "Inequalities and Approximations for the Finite Hilbert Transform: A Survey of Recent Results," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematical Analysis and Applications, pages 53-164, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-31339-5_4
    DOI: 10.1007/978-3-030-31339-5_4
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