Using Fredholm determinants to estimate the smoothness of refinable functions. (English) Zbl 0927.42016

Daubechies, Ingrid

Chui, C. K. (ed.) et al., Approximation theory VIII. Vol. 2. Wavelets and multilevel approximation. Papers from the 8th Texas international conference, College Station, TX, USA, January 8–12, 1995. Singapore: World Scientific. Ser. Approx. Decompos. 6, 89-112 (1995).

Summary: The regularity of refinable functions is linked to the spectral properties of special operators associated to the refinement equation; we then use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases.
For the entire collection see [Zbl 0902.00035].

MSC:

42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60	Numerical methods for wavelets

Keywords:

Fredholm determinants; smoothness; regularity; refinable functions; refinement equation