ENGLISH ABSTRACT: In this thesis we study a wavelet construction procedure based on a multiresolutional method, before specializing to the case of spline wavelets. First, we introduce and analyze the concepts of scaling ...

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In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove ...

ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves and surfaces in computer graphics, by repeatedly applying a subdivision (re ning) scheme to a given set of points. In the literature, ...

We study refinable functions where the dilation factor is not always assumed to be 2. In our investigation, the role of convolutions and refinable step functions is emphasized as a framework for understanding various ...

ENGLISH ABSTRACT: Multi-resolution analysis (MRA) has become a very popular eld of mathematical study in the past two decades, being not only an area rich in applications but one that remains lled with open problems. ...

Subdivision is an important iterative technique for the efficient generation of curves and surfaces in geometric modelling. The convergence of a subdivision scheme is closely connected to the existence of a corresponding ...

This work studies the regularity (or smoothness) of continuous finitely supported refinable functions which are mainly encountered in multiresolution analysis, iterative interpolation processes, signal analysis, etc. ...

Subdivision techniques have, over the last two decades, developed into a powerful tool in computer-aided geometric design (CAGD). In some applications it is required that data be preserved exactly; hence the need for ...

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