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arXiv · 2212.12260

Ellipticity and the problem of iterates in Denjoy-Carleman classes

Stefan Fürdös·Gerhard Schindl
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Abstract

In 1978 M\'etivier 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.

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Stefan Fürdös, Gerhard Schindl. 2022-12-23. Ellipticity and the problem of iterates in Denjoy-Carleman classes. https://doi.org/10.1007/s13348-024-00455-7

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