In this paper we shall study the initial functions in a subdivision scheme in a Sobolev space. By investigating the mutual relations among the initial functions in a subdivision scheme, we are able to study in a relatively uniied approach several questions related to a subdivision scheme in a Sobolev space such as convergence, error estimate and convergence rate of a subdivision scheme in a Sob...

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead o...

We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest to the analysis of convergence and smoothn...

For a non-square transfer matrix with zeros on the extended imaginary axis including infinity, this paper discusses how to dilate (augment) such transfer matrix to a square one without adding extra zeros on the extended imaginary axis. The state-space construction for the dilation is proposed by using the finite and infinite eigenstructures of the transfer matrix. Copyright c © 2002 IFAC

A simple analytic formula for the spectral radius of matrix continuous refinement operators is established. On the space L2 (R),m ≥ 1 and s ≥ 1, their spectral radius is equal to the maximal eigenvalue in magnitude of a number matrix, obtained from the dilation matrix M and the matrix function c defining the corresponding refinement operator. A similar representation is valid for the continuous...

The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute the minimum dilation of embedding circulant net...

Abst rac t . Midimew networks [1] are mesh-connected networks derived from a subset of degree-4 circulant graphs. They have minimum diameter and average distance among all degree-4 circulant graphs, and are better than some of the most common topologies for parallel computers in terms of various cost measures. Among the many midimew networks, the rectangular ones appear to be most suitable for ...