The Overdetermined Cauchy Problem for $\omega$-ultradifferentiable Functions

Abstract

In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasianalytic weight functions $\omega$. 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.

References in corpus (1)

• Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms

Cited by in corpus (1)

• Real Paley-Wiener theorems in spaces of ultradifferentiable functions