23 research outputs found
Hermite subdivision schemes, exponential polynomial generation, and annihilators
We consider the question when the so--called spectral condition} for Hermite
subdivision schemes extends to spaces generated by polynomials and exponential
functions. The main tool are convolution operators that annihilate the space in
question which apparently is a general concept in the study of various types of
subdivision operators. Based on these annihilators, we characterize the
spectral condition in terms of factorization of the subdivision operator
Full rank interpolatory subdivision schemes: Kronecker, filters and multiresolution
AbstractIn this extension of earlier work, we point out several ways how a multiresolution analysis can be derived from a finitely supported interpolatory matrix mask which has a positive definite symbol on the unit circle except at −1. A major tool in this investigation will be subdivision schemes that are obtained by using convolution or correlation operations based on replacing the usual matrix multiplications by Kronecker products
Level-dependent interpolatory Hermite subdivision schemes and wavelets
We study many properties of level-dependent Hermite subdivision, focusing on
schemes preserving polynomial and exponential data. We specifically consider
interpolatory schemes, which give rise to level-dependent multiresolution
analyses through a prediction-correction approach. A result on the decay of the
associated multiwavelet coefficients, corresponding to a uniformly continuous
and differentiable function, is derived. It makes use of the approximation of
any such function with a generalized Taylor formula expressed in terms of
polynomials and exponentials
Multiwavelets : analisi teorica ed algoritmi
Dottorato di ricerca in matematica. 7. ciclo. Tutore L. Montefusco. Coordinatore A. GiambrunoConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
Hermite B-Splines: n-Refinability and Mask Factorization
This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets