Résumé: In this thesis we study the multi-box spline functions which represent piece-wise polynomials on regular meshes. This type of functions has various applications, such as signal processing, data compression, multi-scale methods in numerical analysis and in subdivision in computer aided design [10,7]. A common consequence of studying refinable spaces is the construction of wavelets. These multi-box splines studies can be expressed in different forms, either as piecewise functions, which will be determined by their values at the vertices of all the triangles in the mesh, or by finding their Fourier transforms. The main properties of these polynomials are studied, in particular stability, linear independence and symmetry. We study various examples of multi-box splines, constant, linear, cubic and quadratic multi-box spline functions within a known mesh support and then study their properties. While in different place in this thesis, we study the linear multi-box splines in a different mesh without knowing the values of the function. In order to do that we have to study the jump conditions of the mesh at the non integer points. We also try for the constant case, on concentrating on general constructions rather than isolated examples, and study the main properties of this function.

Langue: Anglais
Collation: 164 p. ill. ;30 cm.
Diplôme: Doctorat
Etablissement de soutenance: Dundee, University of Dundee
Spécialité: Mathématique
Thème Mathématiques

Mots clés:
Stability
Generator
Multi-box spline
Symmetry

Note: Bibliogr. pp.159-165