Wilson Bases Research Articles

Wilson Bases and Modulation Spaces

AbstractWe show that the recently discovered WILSON bases of exponential decay are unconditional bases for all modulation spaces on R, including the classical BESSEL potential spaces, the Segal algebra So, and the SCHWARTZ space. As a consequence we obtain new bases for spaces of entire functions. On the other hand, the WILSON bases are no unconditional bases for the ordinary Lp‐spaces for p ≠ 2.