Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions (Q2136538)
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scientific article; zbMATH DE number 7524874
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions |
scientific article; zbMATH DE number 7524874 |
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Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions (English)
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10 May 2022
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The author considers a class of global pseudo-differential operators of infinite order of Shubin type; the functional framework are the spaces of tempered ultradistributions of Beurling-Björck type. The main results are a formula for the change of quantisation and the construction of parametrices for the pseudo-differential operators with symbols that satisfy hypoellipticity bounds. Of course, the latter implies that these hypoelliptic operators are globally regular on the space of ultradistributions of Beurling-Björck type.
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global classes
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pseudodifferential operator
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quantizations
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hypoellipticity
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