Calder\'on's reproducing formulas for the Weinstein $L^2$- multiplier operators

TL;DR

This paper develops Calderón's reproducing formulas for Weinstein $L^2$-multiplier operators on Euclidean space, utilizing Weinstein transform theory and reproducing kernels to analyze best approximation properties.

Contribution

It introduces Calderón's reproducing formulas specifically for Weinstein $L^2$-multiplier operators, advancing the harmonic analysis framework for this setting.

Findings

Calderón's reproducing formulas are established for Weinstein $L^2$-multipliers.

The paper provides approximation results using Weinstein transform and kernels.

New insights into the harmonic analysis of Weinstein operators are presented.

Abstract

The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calder\'on's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing kernels.