The Continuous Gabor Transform and Smoothness Analysis of Besicovitch Almost Periodic Signals

In this work smoothness analysis of almost-periodic signals is studied. Here, analogously to the case of
$L^{2}$
(JR) or finite energy signals, the smoothness of the class of almost periodic bounded power signals is characterized in terms of the decay of its Gabor transform. Moreover, some results are given as equivalence of norms between appropriate function spaces.