The Theorem of Iterates for elliptic and non-elliptic Operators

Abstract

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case and enables us, for the first time, to prove non-analytic Theorems of Iterates for non-elliptic differential operators. In particular, by generalizing a Theorem of Baouendi and Metivier we obtain the Theorem of Iterates for hypoelliptic analytic operators of principal type with respect to several non-analytic ultradifferentiable structures.

arXiv comment45 pages, published version, minor typos corrected and Introduction revised

References in corpus (14)

• Composition in ultradifferentiable classes
• On quasianalytic local rings
• Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
• Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions
• Extension of Whitney jets of controlled growth
• On subadditivity-like conditions for associated weight functions
• Equivalence of stability properties for ultradifferentiable function classes
• Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions
• On the extension of Whitney ultrajets
• A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions
• On the Borel mapping in the quasianalytic setting
• A characterization of the wave front set defined by the iterates of an operator with constant coefficients
• Geometric Microlocal Analysis in Denjoy-Carleman classes
• Iterates of systems of operators in spaces of $\omega$-ultradifferentiable functions

Cited by in corpus (7)

• On subadditivity-like conditions for associated weight functions
• On the inclusion relations of global ultradifferentiable classes defined by weight matrices
• The Kotake-Narasimhan Theorem in general ultradifferentiable classes
• Ellipticity and the problem of iterates in Denjoy-Carleman classes
• On Orlicz classes defined in terms of associated weight functions
• Construction of the log-convex minorant of a sequence $\{M_{\alpha }{\}}_{\alpha \in {\mathbb{N}}_0^d}$
• Strong factorization of ultradifferentiable vectors associated with compact Lie group representations