Characterizations of derivations on spaces of smooth functions

TL;DR

This paper characterizes when additive operators on spaces of smooth functions are essentially derivations, providing equivalent conditions that identify such operators as multiples of the derivation.

Contribution

It offers a comprehensive set of equivalent conditions to identify derivations among additive operators on smooth function spaces.

Findings

Identifies conditions under which additive operators are derivations

Provides a characterization of derivations on smooth function spaces

Establishes criteria for operators to be multiples of the derivation

Abstract

We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation.