243 research outputs found
Mutual estimates of time-frequency representations and uncertainty principles
In this paper we give different estimates between Lebesgue norms of quadratic
time-frequency representations. We show that, in some cases, it is not possible
to have such bounds in classical spaces, but the Lebesgue norm needs to
be suitably weighted. This leads to consider weights of polynomial type, and,
more generally, of ultradifferentiable type, and this, in turn, gives rise to
use as functional setting the ultradifferentiable classes. As applications of
such estimates we deduce uncertainty principles both of Donoho-Stark type and
of local type for representations
Uncertainty principle, positivity and Lp-boundedness for generalized spectrograms
AbstractIn this paper we are concerned with the properties of positivity, uncertainty principle and continuity in Lp spaces of a generalized spectrogram. In particular we study the connections of a generalized spectrogram, as a subclass of the Cohen class, with the Rihaczek and the Wigner representations. We also consider the behavior of the generalized spectrogram with respect to the positivity and the Lp boundedness of the corresponding localization operators
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