David Jornet

A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions

We give a simple proof of a general theorem of Kotake–Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based on an example of Métivier, we also show that the ellipticity is a necessary condition for the theorem to be true.

The Problem of Iterates in Some Classes of Ultradifferentiable Functions

We consider the problem of iterates in some spaces of ultradifferentiable classes in the sense of Braun, Meise and Taylor. In particular, we obtain a microlocal version, in this setting of functions, of the “Theorem of the iterates of Kotake and Narasimhan”.

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

Abstract We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space S and in the space S ω as introduced by Bjorck for weight functions ω. Several examples are discussed in this new setting.

Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of Type

We study Fredholm (weighted) composition operators between general weighted Banach spaces of analytic functions on the open unit disc with sup-norms.