Uncertainty product of spherical wavelets
Ilona Iglewska-Nowak
TL;DR
This paper analyzes the asymptotic behavior of the uncertainty product for a family of spherical wavelets, including popular types like Gauss-Weierstrass and Mexican needlets, revealing boundedness properties.
Contribution
It computes the asymptotic behavior of the uncertainty product for various spherical wavelets and identifies which wavelets have bounded uncertainty constants.
Findings
Asymptotic behavior of the uncertainty product is characterized.
Boundedness of the uncertainty constant varies among wavelets.
Includes analysis of popular wavelets like Gauss-Weierstrass and Mexican needlets.
Abstract
In the paper, asymptotic behavior of the uncertainty product for a family of zonal spherical wavelets is computed. The family contains the most popular wavelets, such as Gauss-Weierstrass, Abel-Poisson and Poisson wavelets and Mexican needlets. Boundedness of the uncertainty constant is in general not given, but it is a property of some of the wavelets from this class.
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