Dunkl Linear Canonical Wavelet Transform: Concentration Operators and Applications to Scalogram and Localized Functions

In the present paper we study a class of Toeplitz operators called concentration operators that are self-adjoint and compact in the linear canonical Dunkl setting. We show that a finite vector space spanned by the first eigenfunctions of such operators is of a maximal phase-space concentration and has the best phase-space concentrated scalogram inside the region of interest. Then, using these eigenfunctions, we can effectively approximate functions that are essentially localized in specific regions, and corresponding error estimates are given. These research results cover in particular the classical and the Hankel settings, and have potential application values in fields such as signal processing and quantum physics, providing a new theoretical basis for relevant research.