Uncertainty constants and quasispline wavelets

TL;DR

This paper introduces quasispline wavelets with uncertainty constants that approach those of Meyer wavelets, contrasting with traditional wavelets whose uncertainty constants grow unbounded with increased smoothness.

Contribution

The paper constructs a new class of wavelets, quasispline wavelets, whose uncertainty constants remain bounded and approach Meyer wavelet values, unlike classical wavelets.

Findings

Uncertainty constants of quasispline wavelets tend to Meyer wavelet constants.

Class of wavelets with bounded uncertainty constants.

Contrast with classical wavelets where uncertainty constants grow infinitely.

Abstract

In 1996 Chui and Wang proved that the uncertainty constants of scaling and wavelet functions tend to infinity as smoothness of the wavelets grows for a broad class of wavelets such as Daubechies wavelets and spline wavelets. We construct a class of new families of wavelets (quasispline wavelets) whose uncertainty constants tend to those of the Meyer wavelet function used in construction.