Two-wavelet theory and two-wavelet localization operators on the q-Dunkl harmonic analysis.

In this paper, using the q -Dunkl harmonic analysis introduced in Bettaibi and Bettaieb [q-Analog of the Dunkl transform on the real line, Tamsui Oxf. J. Math. Sci. 25(2) (2007) 117–205] and motivated by Wong's approach [M. W. Wong, Wavelet Transforms and Localization Operators, Vol. 136 (Springer Science & Business Media, Berlin, 2002)], we first define and study the q -wavelets, the continuous q -wavelet transforms. Next, we introduce the two-wavelet localization operators, the Schatten–von Neumann properties of these localization operators are established, and for trace class localization operators, the traces and the trace class norm inequalities are presented. [ABSTRACT FROM AUTHOR]