Matrix transform of irregular weyl-heisenberg wave packet frames for L² (R)

Abstract

Cordoba and Fefferman [4] introduced wave packet systems by applying certain collections of dilations, modulations and translations to the Gaussian function in the study of some classes of singular integral operators. In this paper, we introduce the concept of matrix transform M = (?p,q,r,j,k,m) and with the help of matrix transform we study the action of M on f ? L2 (R) and on its wave packet coefficients. Further, we also obtain the tight frame condition for matrix transform of f ? L2 (R) whose wave packet series expansion is known.