Importance of Zak transforms for harmonic analysis
The author proves the Plancherel theorem for locally compact Abelian (LCA) groups via Zak transforms, based on the fact that Fourier integrals are averages of Zak transforms for any choice of a lattice. He also derives and applies generalized Zak transforms intertwining certain unitary representations of LCA groups with modulation representations.
scientific article; zbMATH DE number 6042805