arXiv subjects

Chiara Boiti

Publications and source records attributed to Chiara Boiti.

21 records · Page 2Linked to original sources

arXiv2016

Iterates of systems of operators in spaces of $ω$-ultradifferentiable functions

Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal E}_ω^P$ and ${\mathcal E}_ω^Q$ of $ω$-ultradifferentiable functions with respect to the iterates of the systems $P$ and $Q$ respectively. We find necessary and sufficient conditions, on the systems and on the weights $ω(t)$ and $σ(t)$, for the inclusion ${\mathcal E}_ω^P\subseteq{\mathcal E}_σ^Q$. As a consequence we have a generalization of the classical Theorem of the Iterates.

math.FA↗

arXiv2015

The Overdetermined Cauchy Problem for $ω$-ultradifferentiable Functions

In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $ω$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasianalytic weight functions $ω$. We show that existence of solutions of the Cauchy problem is equivalent to the validity of a Phragmén-Lindelöf principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties.

math.AP↗

arXiv2014

A characterization of the wave front set defined by the iterates of an operator with constant coefficients

We characterize the wave front set $WF^P_\ast(u)$ with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution $u\in{\mathcal D}'(Ω)$, $Ω$ an open subset in ${\mathbb R}^n$. We use recent Paley-Wiener theorems for generalized ultradifferentiable classes in the sense of Braun, Meise and Taylor. We also give several examples and applications to the regularity of operators with variable coefficients and constant strength. Finally, we construct a distribution with prescribed wave front set of this type.

math.AP↗