Segal-Bargmann transform and Paley-Wiener theorems on $M(2).$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230643We study the Segal-Bargmann transform on $M(2).$ The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are studied. Using a Gutzmer type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of $M(2).$ We also prove a Paley-Wiener theorem for the inverse Fourier transformFunctional Analysis22E30Segal-Bargmann transform and Paley-Wiener theorems on $M(2).$text