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Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions

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Abstract

We develop a theory of pseudodifferential operators of infinite order for the global classes \(\mathcal {S}_{\omega }\) of ultradifferentiable functions in the sense of Björck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.

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Acknowledgements

The first author was partially supported by the project GV Prometeo 2017/102, and the second author by the project MTM2016-76647-P. This article is part of the PhD. Thesis of V. Asensio. The authors are very grateful to the two referees for the careful reading and their suggestions and comments, which improved the paper.

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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 & David Jornet

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  1. Vicente Asensio
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  2. David Jornet
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Correspondence to David Jornet.

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Asensio, V., Jornet, D. Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. RACSAM 113, 3477–3512 (2019). https://doi.org/10.1007/s13398-019-00710-8

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  • DOI: https://doi.org/10.1007/s13398-019-00710-8

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