A Gevrey Differential Complex on the Torus

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To a system of n closed one-forms on the torus \({\mathbb {T}}^{m+n}\), we associate a differential complex and compute the induced cohomology groups in the s-Gevrey category, provided that a related matrix of periods satisfies a Diophantine condition. Also, we present a complete characterization for the s-global hypoellipticity at the level of q-forms for \(q\ge 0\).

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Correspondence to A. Meziani.

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P. L. Dattori da Silva was supported in part by CNPq (grant 309496/2018-7) and FAPESP (grants 2018/15046-0 and 2018/14316-3).

Communicated by Fabio Nicola.

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da Silva, P.L.D., Meziani, A. A Gevrey Differential Complex on the Torus. J Fourier Anal Appl 26, 8 (2020) doi:10.1007/s00041-019-09713-w

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  • Differential complex
  • Solvability
  • Hypoellipticity
  • Fourier series
  • Diophantine condition

Mathematics Subject Classification

  • Primary 58J10
  • Secondary 35F35