243 research outputs found

    Mutual estimates of time-frequency representations and uncertainty principles

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    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 LpL^p 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

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    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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