# Besov-Dunkl Spaces connected with generalized Taylor formula on the real line

## TL;DR

This paper introduces Besov-Dunkl spaces on the real line linked to a generalized Taylor formula, characterizing these spaces through Dunkl convolution and expanding the functional analysis framework in this context.

## Contribution

It defines Besov-Dunkl spaces associated with Dunkl translation operators and characterizes them via Dunkl convolution, extending classical analysis tools.

## Key findings

- Defined Besov-Dunkl spaces on the real line.
- Characterized these spaces using Dunkl convolution.
- Connected the spaces with a generalized Taylor formula.

## Abstract

In the present paper, we define for the Dunkl tranlation operators on the real line, the Besov-Dunkl space of functions for which the remainder in the generalized Taylor's formula has a given order. We provide characterization of these spaces by the Dunkl convolution.