Spectral Theorems in the Laguerre Hypergroup Setting

We introduce the two-wavelet multiplier operator in the Laguerre hypergroup setting. Knowing the fact that the study of this operator are both theoretically interesting and practically useful, we investigated several subjects of spectral analysis for the new operator. Firstly, we present a comprehensive analysis of the generalized two-wavelet multiplier operator. Next, we introduce and we study the generalized Landau-PollakSlepian operator. As applications, some problems of the approximation theory and the uncertainty principles are studied. Finally, we give many results on the boundedness and compactness of the Laguerre two-wavelet multipliers on Lpα(K), 1≤p≤∞.