Abstract
We define the localization operators associated with Laguerre wavelet transforms. Next, we prove the boundedness and compactness of these operators, which depend on a symbol and two admissible wavelets on Lpα(K), 1 ≤ p ≤ ∞.
Highlights
Let Hd be the (2d + 1)-dimensional Heisenberg group with the multiplication law (z, t)(z, t ) = (z + z, t + t − Im(zz ))
Following [29], in this paper we identify the dual of the Laguerre hypergroup by K := R × N
Time-frequency localization operators are a mathematical tool to define a restriction of functions to a region in the time-frequency plane that is compatible with the uncertainty principle and to extract time-frequency features
Summary
Time-frequency localization operators are a mathematical tool to define a restriction of functions to a region in the time-frequency plane that is compatible with the uncertainty principle and to extract time-frequency features In this sense, these operators have been introduced and studied by Daubechies [9, 10, 11] and Ramanathan and Topiwala [30], and they are extensively investigated as an important mathematical tool in signal analysis and other applications [17, 12, 13, 35, 7]. As the harmonic analysis on the Laguerre hypergroup has known remarkable development, it is natural to ask whether there exists the equivalent of the theory of localization operators for the continuous wavelet transform related to this harmonic analysis.
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