Abstract
We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. We present an approach by combining a characterization of these spaces via eigenfuction expansions, generated by an elliptic operator, and the analysis of matrix-symbols obtained by these expansions.
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Acknowledgements
The authors wish to thank Alexandre Kirilov and Wagner A.A. de Moraes for useful discussions and suggestions.
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The second author was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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de Ávila Silva, F., Machado, E.C. Global ultradifferentiable hypoellipticity on compact manifolds. Arch. Math. 118, 615–624 (2022). https://doi.org/10.1007/s00013-022-01719-z
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DOI: https://doi.org/10.1007/s00013-022-01719-z