We investigate interpolatory multiscale transformations for functions between manifolds which are based on interpolatory subdivision rules. We characterize the HölderZygmund smoothness of a function between manifolds in terms of the coe cient decay w.r.t. this multiscale transform.

Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reprod...

A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The C and C convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the c...

1 Interpolatory basis function 2 (t) and its rst and second derivatives 0 2 (t) and 00 2 (t). 11 2 Interpolation of the function f(t) = e t sin(t); t = 0; 0:125; 0:25; :::; 10 (solid line) using the interpolatory subdivision scheme (dotted line) and the Shannon bases sinc(t) (shown using points). The interpolating points are taken at t = 0 Abstract The initialization of wavelet transforms and t...

In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. It is shown that the interpolatory schemes are (mostly) capable of generating the same functional space as the approximating one. Moreover, the interplay between str...

We analyse the approximation and smoothness properties of fundamental and refinable functions that arise from interpolatory subdivision schemes in multidimensional spaces. In particular, we provide a general way for the construction of bivariate interpolatory refinement masks such that the corresponding fundamental and refinable functions attain the optimal approximation order and smoothness or...

In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the ful...