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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 2, 2001, pp. 505–512
DOI: 10.4171/ZAA/1027

Published online: 2001-06-30

The Generalized Riemann Problem of Linear Conjugation for Polyanalytic Functions of Order $n$ in $W_{n,p}(D)$

Ali Seif Mshimba[1]

(1) University of Dar es Salaam, Tanzania

We consider a homogeneous polyanalytic differential equation of order $n$ in a simply-connected domain $D$ with a smooth boundary $\partial D$ in the complex plane $\mathbb C$. We pose and then prove solvability of a generalized Riemann problem of linear conjugation to the differential equation. This is done by reducing the problem into $n$ classical Riemann problems of linear conjugation for holomorphic functions, the solution of which is available in the literature.

Keywords: Polyanalytic functions, Riemann problem of linear conjugation

Mshimba Ali Seif: The Generalized Riemann Problem of Linear Conjugation for Polyanalytic Functions of Order $n$ in $W_{n,p}(D)$. Z. Anal. Anwend. 20 (2001), 505-512. doi: 10.4171/ZAA/1027