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Filbir, F. ; Occorsio, D.* ; Themistoclakis, W.*

Approximation of finite Hilbert and Hadamard transforms by using equally spaced nodes.

Mathematics 8:542 (2020)
Verlagsversion DOI
Open Access Gold
Creative Commons Lizenzvertrag
In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [-1,1] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Hilbert Transform ; Hadamard Transform ; Hypersingular Integral ; Bernstein Polynomials ; Boolean Sum ; Simultaneous Approximation ; Equidistant Nodes; Numerical Evaluation; Integral-equations; Bernstein; Operators
ISSN (print) / ISBN 2227-7390
e-ISSN 2227-7390
Zeitschrift Mathematics
Quellenangaben Band: 8, Heft: 4, Seiten: , Artikelnummer: 542 Supplement: ,
Verlag MDPI
Verlagsort Basel, Switzerland
Begutachtungsstatus Peer reviewed