This article presents a systematic study for abstract harmonic analysis aspects of wave-packet transforms over locally compact abelian (LCA) groups. Let be a locally compact group, let be an LCA group, and let be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by , and we study basic properties of wave-packet groups. Then we study theoretical aspects of wave-packet transforms. Finally, we will illustrate application of these techniques in the case of some well-known examples.
"Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups." Banach J. Math. Anal. 11 (1) 50 - 71, January 2017. https://doi.org/10.1215/17358787-3721281