ABSTRACT

Abstract. We study special functions obtained as limits of dyadic and p / q -adic subdivision schemes in one dimension. While the former are used for designing compactly supported wavelet bases, the latter are a flexible generalization which has already found application in digital signal pro­ cessing. For q > 1, however, we obtain an infinite set of different limit functions instead of shifted copies of a single one, and a direct application of former ideas becomes impossible. However, our “discrete” approach allows us to extend the results of Daubechies and Lagarias (on Holder regularity estimates based on infinite products of matrices) to p / q -adic schemes. We obtain easily implementable, sharp Holder regularity esti­ mates.