On uniform approximation by polyanalytic polynomials and the Dirichlet problem for bianalytic functions

New necessary and sufficient conditions for the uniform approximability of functions by polyanalytic polynomials and polyanalytic rational functions on compact subsets of the plane are established. Connections between these approximation problems and the Dirichlet problem for bianalytic functions ar...

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Bibliographic Details
Published in:Sbornik. Mathematics 2002-10, Vol.193 (10)
Main Authors: Carmona, J J, Paramonov, P V, Fedorovskii, K Yu
Format: Article
Language:English
Subjects:
APPROXIMATIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRICHLET PROBLEM
POLYNOMIALS
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Summary:New necessary and sufficient conditions for the uniform approximability of functions by polyanalytic polynomials and polyanalytic rational functions on compact subsets of the plane are established. Connections between these approximation problems and the Dirichlet problem for bianalytic functions are also analysed.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2002V193N10ABEH000690;COUNTRYOFINPUT:INTERNATIONALATOMICENERGYAGENCY(IAEA)