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

J. J. Carmona   ; P. V. Paramonov   ; K. Yu. Fedorovskiy

Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1469-1492

Résumé

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.

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