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Approximation of the Hilbert Transform on the real line using Hermite zeros


Authors: M. C. De Bonis, B. Della Vecchia and G. Mastroianni
Journal: Math. Comp. 71 (2002), 1169-1188
MSC (2000): Primary 65D30, 41A05
DOI: https://doi.org/10.1090/S0025-5718-01-01338-2
Published electronically: October 25, 2001
MathSciNet review: 1898749
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Abstract: The authors study the Hilbert Transform on the real line. They introduce some polynomial approximations and some algorithms for its numerical evaluation. Error estimates in uniform norm are given.


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Additional Information

M. C. De Bonis
Affiliation: Dipartimento di Matematica, Università della Basilicata, C/da Macchia Romana 85100 Potenza, Italy
Email: mdebonis@pta.unibas.it

B. Della Vecchia
Affiliation: Dipartimento di Matematica, Istituto G. Castelnuovo, Università di Roma La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
Email: dellavecchia@iamna.iam.na.cnr.it

G. Mastroianni
Affiliation: Dipartimento di Matematica, Università della Basilicata, C/da Macchia Romana 85100 Potenza, Italy
Email: mastroianni@unibas.it

DOI: https://doi.org/10.1090/S0025-5718-01-01338-2
Keywords: Hilbert Transform, orthonormal polynomials, Gaussian quadrature rules, product quadrature rules
Received by editor(s): April 9, 1998
Received by editor(s) in revised form: December 8, 1999, May 12, 2000, and August 18, 2000
Published electronically: October 25, 2001
Additional Notes: This work was supported by M.U.R.S.T. (ex. 40%)
Article copyright: © Copyright 2001 American Mathematical Society

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