169 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
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
Extended Hermite Subdivision Schemes
International audienceSubdivision schemes are efficient tools for building curves and surfaces. For vector subdivision schemes, it is not so straightforward to prove more than the Hölder regularity of the limit function. On the other hand, Hermite subdivision schemes produce function vectors that consist of derivatives of a certain function, so that the notion of convergence automatically includes regularity of the limit. In this paper, we establish an equivalence betweena spectral condition and operator factorizations, then we study how such schemes with smooth limit functions can be extended into ones with higher regularity. We conclude by pointing out this new approach applied to cardinal splines
- …