Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. (English) Zbl 1432.35050
A method based on the study of the properties of the Wigner transform is used to obtain classes (in 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.
Reviewer: Mihai Pascu (Bucureşti)
MSC:
| 35G05 | Linear higher-order PDEs |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 47F05 | General theory of partial differential operators |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
Keywords:
regularity; partial differential operators with polynomial coefficients; Wigner transform; Schwartz spaces; weighted spacesCitations:
Zbl 0616.47040References:
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