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Quantizations and Global Hypoellipticity for Pseudodifferential Operators of Infinite Order in Classes of Ultradifferentiable Functions

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Abstract

We study the change of quantization for a class of global pseudodifferential operators of infinite order in the setting of ultradifferentiable functions of Beurling type. The composition of different quantizations as well as the transpose of a quantization are also analysed, with applications to the Weyl calculus. We also compare global \(\omega \)-hypoellipticity and global \(\omega \)-regularity of these classes of pseudodifferential operators.

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Acknowledgements

The author was supported by the projects GV PROMETEO/2017/102 and PROMETEO/2021/070. He is greatly indebted to David Jornet for his helpful comments and ideas, and for the careful reading of the paper. The author would also like to thank Chiara Boiti for the revision of the paper. This is part of the author’s Ph.D. Thesis.

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

    Vicente Asensio

  2. Centro Universitario EDEM Muelle de la Aduana, s/n, La Marina de Valencia, 46024, Valencia, Spain

    Vicente Asensio

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  1. Vicente Asensio
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Asensio, V. Quantizations and Global Hypoellipticity for Pseudodifferential Operators of Infinite Order in Classes of Ultradifferentiable Functions. Mediterr. J. Math. 19, 135 (2022). https://doi.org/10.1007/s00009-022-02034-1

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  • DOI: https://doi.org/10.1007/s00009-022-02034-1

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