The Kotake-Narasimhan Theorem in general ultradifferentiable classes

TL;DR

This paper extends the Kotake-Narasimhan theorem to general ultradifferentiable classes defined by weight matrices, generalizing previous results for classes defined by weight sequences and functions, including a sharp result for Beurling classes.

Contribution

It generalizes the Kotake-Narasimhan theorem to ultradifferentiable classes via weight matrices, unifying and extending prior results for weight sequences and functions.

Findings

Established a generalized Kotake-Narasimhan theorem for ultradifferentiable classes.

Recovered known results for weight sequence and weight function classes.

Provided a sharp theorem for Beurling classes.

Abstract

We prove a Kotake-Narasimhan type theorem in general ultradifferentiable classes given by weight matrices. In doing so we simultaneously recover and partially generalize the known results for classes given by weight sequences and weight functions. In particular, we obtain a sharp Kotake-Narasimhan theorem for Beurling classes.