Two-Wavelet Multipliers and Applications

Abstract

This paper delves into the Dunkl-Bessel operator on and its corresponding harmonic analysis. A generalized form of Heisenberg-type uncertainty inequality is established. Schatten-von Neumann properties for the two-wavelet multiplier within the Dunkl-Bessel theory framework are elucidated. Additionally, the trace formula for a two-wavelet Dunkl-Bessel multiplier is proven as a bounded linear operator in the trace class from into . Furthermore, subject to appropriate conditions, the boundedness and compactness of these Dunkl-Bessel two-wavelet multipliers are proven, applicable to , 1 ≤ p ≤ ∞. Finally, using a class of concentration operators for the Dunkl-Bessel two-wavelet, we show that the eigenfunctions of the Dunkl-Bessel two-wavelet are maximally concentrated in the time-frequency domain. Leveraging this result, we derive approximation inequalities for functions that exhibit significant concentration within specific regions of the time-frequency plane.