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INICIO | 19 de mayo de 2024
  

Wavelets on the integers.

Título inglés Wavelets on the integers.
Título español Ondículas sobre los enteros.
Autor/es Gressman, Philip
Organización Dep. Math. Washington Univ., St. Louis (Missouri), Estados Unidos
Revista 0010-0757
Publicación 2001, 52 (3): 257-288, 4 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2 = TD. We choose to define dyadic dilations on the integers in terms of this functional equation. All such dyadic dilations are characterized and the corresponding multiresolution structures they generate are introduced and examined. The main results of this paper focus on connecting multiresolution structures and wavelets on the integers with their counterparts on the line and include the fact that every wavelet on the integers is a MRA wavelet.
Clasificación UNESCO 120213
Palabras clave español Ondículas ; Análisis de Fourier ; Métodos numéricos
Código MathReviews MR1885222
Código Z-Math Zbl 0996.42024
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es