9,514 research outputs found
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of
uncertainty principles and localization, emphasize their mutual connections and
investigate practical consequences. The discussion is strongly oriented
towards, and motivated by signal processing problems, from which significant
advances have been made recently. Relations with sparse approximation and
coding problems are emphasized
Uncertainty principles for integral operators
The aim of this paper is to prove new uncertainty principles for an integral
operator with a bounded kernel for which there is a Plancherel theorem.
The first of these results is an extension of Faris's local uncertainty
principle which states that if a nonzero function is
highly localized near a single point then cannot be concentrated in a
set of finite measure. The second result extends the Benedicks-Amrein-Berthier
uncertainty principle and states that a nonzero function
and its integral transform cannot both have support of finite
measure. From these two results we deduce a global uncertainty principle of
Heisenberg type for the transformation . We apply our results to obtain a
new uncertainty principles for the Dunkl and Clifford Fourier transforms
Generalized Analogs of the Heisenberg Uncertainty Inequality
We investigate locally compact topological groups for which a generalized
analogue of Heisenberg uncertainty inequality hold. In particular, it is shown
that this inequality holds for (where is a
separable unimodular locally compact group of type I), Euclidean Motion group
and several general classes of nilpotent Lie groups which include thread-like
nilpotent Lie groups, -NPC nilpotent Lie groups and several low-dimensional
nilpotent Lie groups
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