Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms (Q321849)
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scientific article; zbMATH DE number 6638950
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms |
scientific article; zbMATH DE number 6638950 |
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Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms (English)
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14 October 2016
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A method based on the study of the properties of the Wigner transform is used to obtain classes (in \textit{M. A. Shubin}'s sense [Pseudodifferential operators and spectral theory. Transl. from the Russian by Stig I. Andersson. Berlin etc.: Springer-Verlag (1987; Zbl 0616.47040)]) of partial differential operators with polynomial coefficients. Regularity results in weighted Björk spaces \(\mathcal{S}_{\omega}\) are also obtained. Examples of regular operators which are not globally hypoelliptic are given.
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regularity
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partial differential operators with polynomial coefficients
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Wigner transform
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Schwartz spaces
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weighted spaces
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