Wavelet multipliers in the linear canonical Dunkl setting and applications

The linear canonical Dunkl transform (LCDT) is a novel addition to the class of linear canonical transforms, which has gained a respectable status in the realm of harmonic analysis within a short span of time. Knowing the fact that the study of the theory of the wavelet multipliers is both theoretically interesting and practically useful, we investigate this theory for the LCDT. First, we introduce the notion of the linear canonical Dunkl multiplier and examine the underlying theory of the two-wavelet linear canonical Dunkl multiplier operator. Particularly, we study the trace class properties of such operators and also demonstrate that they belong to the Schatten–von Neumann class. Second, special attention is paid to the boundedness and compactness of the proposed operators on [Formula: see text], [Formula: see text]. We culminate our study by formulating several typical examples of the two-wavelet LCDMO and some applications.