A NEW TECHNIQUE TO ESTIMATE THE REGULARITY OF REFINABLE FUNCTIONS

Authors
COHEN A DAUBECHIES I
Citation
A. Cohen et I. Daubechies, A NEW TECHNIQUE TO ESTIMATE THE REGULARITY OF REFINABLE FUNCTIONS, Revista matematica iberoamericana, 12(2), 1996, pp. 527-591
Citations number
48
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Revista matematica iberoamericana → ACNP
ISSN journal
02132230
Volume
12
Issue
2
Year of publication
1996
Pages
527 - 591
Database
ISI
SICI code
0213-2230(1996)12:2<527:ANTTET>2.0.ZU;2-Q
Abstract
We study the regularity of refinable functions by analyzing the spectr al properties of special operators associated to the refinement equati on; in particular, we use the Fredholm determinant theory to derive nu merical estimates for the spectral radius of these operators in certai n 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.