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| Format: | Preprint |
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2022
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| Accès en ligne: | https://arxiv.org/abs/2212.12260 |
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| _version_ | 1866912197868781568 |
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| author | Fürdös, Stefan Schindl, Gerhard |
| author_facet | Fürdös, Stefan Schindl, Gerhard |
| contents | In 1978 Métivier showed that a differential operator $P$ with analytic coefficients is elliptic if and only if the theorem of iterates holds for $P$ with respect to any non-analytic Gevrey class. In this paper we extend this theorem to Denjoy-Carleman classes given by strongly non-quasianalytic weight sequences. The proof involves a new way to construct optimal functions in Denjoy-Carleman classes, which might be of independent interest. Moreover, we point out that the analogous statement for Braun-Meise-Taylor classes given by weight functions cannot hold. This signifies an important difference in the properties of Denjoy-Carleman classes and Braun-Meise-Taylor classes, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12260 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ellipticity and the problem of iterates in Denjoy-Carleman classes Fürdös, Stefan Schindl, Gerhard Analysis of PDEs 35B65 (Primary) 26E10, 35J99, 46E10 (Secondary) In 1978 Métivier showed that a differential operator $P$ with analytic coefficients is elliptic if and only if the theorem of iterates holds for $P$ with respect to any non-analytic Gevrey class. In this paper we extend this theorem to Denjoy-Carleman classes given by strongly non-quasianalytic weight sequences. The proof involves a new way to construct optimal functions in Denjoy-Carleman classes, which might be of independent interest. Moreover, we point out that the analogous statement for Braun-Meise-Taylor classes given by weight functions cannot hold. This signifies an important difference in the properties of Denjoy-Carleman classes and Braun-Meise-Taylor classes, respectively. |
| title | Ellipticity and the problem of iterates in Denjoy-Carleman classes |
| topic | Analysis of PDEs 35B65 (Primary) 26E10, 35J99, 46E10 (Secondary) |
| url | https://arxiv.org/abs/2212.12260 |