Generalized Taylor formula with integral remainder for Besov-Dunkl spaces

TL;DR

This paper develops a generalized Taylor formula with an integral remainder for Dunkl operators on the real line and characterizes Besov-Dunkl spaces based on the order of the remainder.

Contribution

It introduces a new generalized Taylor formula with integral remainder for Dunkl operators and describes Besov-Dunkl spaces linked to the remainder's order.

Findings

Established properties and estimates of the integral remainder

Characterized Besov-Dunkl spaces according to the order of the remainder

Extended classical Taylor formulas to the Dunkl operator setting

Abstract

In the present paper, we propose to prove some properties and estimates of the integral remainder in the generalized Taylor formula associated to the Dunkl operator on the real line and to describe the Besov-Dunkl spaces for which the remainder has a given order.