Resumen de Time-frequency partitions for the Gelfand triple (S~0, L^2, S~0^1)

H. G. Feichtinger, M. Dorfler

• We give a new characterization of the Gelfand triple of function spaces in (S0,L2,S′0) by means of a family of time-frequency localization operators. The localization operators are defined by the short-time Fourier transform and determine the local time-frequency behavior, whereas the global time-frequency distribution is characterized by a sequence space norm. We also show that the alternative time-frequency localization method with the Weyl transform fails to yield a similar characterization of time-frequency distribution.