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Sur les ensembles d'entiers reconnaissables

Fabien Durand — 1998

Journal de théorie des nombres de Bordeaux

Soient U et V deux systèmes de numération de Bertrand, α et β deux β -nombres multiplicativement indépendants tels que L ( U ) = L ( α ) et L ( V ) = L ( β ) , et E un sous-ensemble de ℕ . Si E est U -reconnaissable et V -reconnaissable alors E est une réunion finie de progressions arithmétiques.

Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.

Sylvie Durand — 1996

Revista Matemática Iberoamericana

The aim of this paper is the study of the convergence of algorithms involved in the resolution of two scale equations. They are fixed point algorithms, often called cascade algorithms, which are used in the construction of wavelets. We study their speed of convergence in Lebesgue and Besov spaces, and show that the quality of the convergence depends on two independent factors. The first one, as we could foresee, is the regularity of the scaling function which is the solution of the equation. The...

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