Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions

Vicente Asensio

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arXiv · 2104.09198

Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions

Vicente Asensio

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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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Vicente Asensio. 2021-04-19. Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions. https://arxiv.org/abs/2104.09198

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