On the regularity of wavelets

Abstract

The regularity index alpha /sub N/ of the scaling functions /sub N/ phi , N=2, 3, . . . of multiresolution analysis introduced by I. Daubechies (1988) is investigated. It is shown that 0.51< alpha /sub 2/<0.53 and lim/sub N to infinity / alpha /sub N//N=1 -log 3/(2 log 2).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>