Abstract
We present sufficient conditions to have global hypoellipticity for a class of Vekua-type operators defined on a compact Lie group. When the group has the property that every non-trivial representation is not self-dual, we show that these sufficient conditions are also necessary. We also present results about the global solvability for this class of operators.
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The author would like to thank Alexandre Kirilov and Ricardo Paleari da Silva for comments and suggestions.
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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)—Finance Code 001 and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant Number 01M01021)
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de Moraes, W.A.A. Regularity of solutions to a Vekua-type equation on compact Lie groups. Annali di Matematica 201, 379–401 (2022). https://doi.org/10.1007/s10231-021-01120-7
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DOI: https://doi.org/10.1007/s10231-021-01120-7