Uncertainty product of spherical wavelets

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.

12 pages

References in corpus (7)

• Continuous Wavelets on Compact Manifolds
• Continuous wavelet transforms on $n$-dimensional spheres
• Poisson wavelets on $n$-dimensional spheres
• Frames of directional wavelets on $n$-dimensional spheres
• Semi-continuous and discrete wavelet frames on $n$-dimensional spheres
• Multiresolution on n-dimensional spheres
• Uncertainty of Poisson wavelets