On the asymptotics of matrix coefficients of representations of SL(2,R)

We study matrix coefficients of the unitary (and also the completely bounded) representations of SL(2,R) and its universal covering group. We describe the asymptotic distribution of column vectors in terms of Whittaker functions, exhibiting also a relationship to the Fourier transform. •Matrix coefficients of representations for universal covering group of SL(2,R).•Approximation of matrix coefficients by Whittaker functions.•Discussion of approximation methods for matrix coefficients.•Discussion of Lp-conditions for matrix coefficients.