Multiplication and convolution topological algebras in spaces of $\omega$-ultradifferentiable functions of Beurling type

TL;DR

This paper characterizes multiplication and convolution topological algebras within spaces of ω-ultradifferentiable functions of Beurling type, analyzing their continuity properties and establishing foundational algebraic structures.

Contribution

It provides a detailed description of the algebraic and topological properties of these function spaces, including conditions for hypocontinuity and discontinuity of operations.

Findings

Identified conditions for multiplication and convolution to form topological algebras.

Analyzed hypocontinuity and discontinuity of algebraic operations.

Established foundational properties of ω-ultradifferentiable function spaces.

Abstract

We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.