MATRIX TRANSFORM OF IRREGULAR WEYL-HEISENBERG WAVE PACKET FRAMES FOR L2(R)

Abstract

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