Time-Frequency Concentration Associated with the Multidimensional Hankel-Wavelet Transform

Abstract

The main goal of this paper is to define a new integral transform called the multidimensional Hankel-wavelet transform and to give some new results related to this transform as generalized Parseval’s, Plancherel’s, inversion and Calderon’s reproducing formulas. Next, we analyse the concentration of this transform on set of finite measure and we give uncertainty principle for orthonormal sequences. Last, we introduce a new class of pseudo-differential operator L_u,v(σ) called localization operator which depend on a symbol σ and two functions u and v, we give a criteria in terms of the symbol σ for its boundedness and compactness, we also show that this operator belongs to the Schatten-Von Neumann classes S p for all p∈[1;+∞] and we give a trace formula.