Year: 2024
Type: article
Abstract: In 1978 Métivier showed that a linear 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 via Fourier integrals, 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.
Source: Collectanea mathematica
Authors: Stefan Fürdös, Gerhard Schindl
Institutions: University of Vienna, Universidade de São Paulo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funders: Austrian Science Fund, Universität Wien
OpenAlex ID: W4402950273