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Schwarz boundary value problems for polyanalytic equation in a sector ring

In this article,we first give a modified Schwarz-Pompeiu formula in a general sector ring by proper conformal mappings, and obtain the solution of the Schwarz problem for the Cauchy-Riemann equation in explicit forms. Furthermore, a class of integral operators is introduced together with their properties. Finally, by virtue of these operators, Schwarz problems for a inhomogeneous polyanalytic equation and for a generalized polyanalytic equation are investigated, respectively.

preprint2022arXivOpen access
Zhihua DuYing WangMin Ku
math.CV
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Open access3 authors1 topic
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Zhihua DuYing WangMin Ku

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