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In this note, we investigate Vekua-type periodic operators of the form$Pu=Lu-Au-B\bar u$, where $L$ is a constant coefficient partial differentialoperator. We provide a complete characterization of the necessary andsufficient conditions for the solvability and global hypoellipticity of $P$. Asan application, we provide a comprehensive characterization of Vekua-typeoperators associated with classical wave, heat, and Laplace equations.

Solvability of Vekua-type periodic operators and applications to classical equations