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A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions

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Abstract

We give a simple proof of a general theorem of Kotake–Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based on an example of Métivier, we also show that the ellipticity is a necessary condition for the theorem to be true.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli n. 30, 44121, Ferrara, Italy

    Chiara Boiti

  2. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, 46071, Valencia, Spain

    David Jornet

Authors
  1. Chiara Boiti
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  2. David Jornet
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Correspondence to David Jornet.

Additional information

C. Boiti and D. Jornet were partially supported by the INdAM-GNAMPA Projects 2014 and 2015. D. Jornet was partially supported by MINECO, Project MTM2013-43540-P.

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Boiti, C., Jornet, D. A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions. J. Pseudo-Differ. Oper. Appl. 8, 297–317 (2017). https://doi.org/10.1007/s11868-016-0163-y

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  • DOI: https://doi.org/10.1007/s11868-016-0163-y

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