Connectivity, homotopy degree, and other properties of α-localized wavelets on R.

Título inglés Connectivity, homotopy degree, and other properties of α-localized wavelets on R.
Título español Conectividad, grado de homotopía y otras propiedades de las ondículas α-localizadas en R.
Autor/es Garrigós, Gustavo
Organización Dip. Mat. Politec. Torino, Turín, Italia
Revista 0214-1493
Publicación 1999, 43 (1): 303-340, 12 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper, we study general properties of α-localized wavelets and multiresolution analyses, when 1/2 < α ≤ ∞. Related to the latter, we improve a well-known result of A. Cohen by showing that the correspondence m → φ' = Π1 m(2−j ·), between low-pass filters in Hα(T) and Fourier transforms of α-localized scaling functions (in Hα(R)), is actually a homeomorphism of topological spaces. We also show that the space of such filters can be regarded as a connected infinite dimensional manifold, extending a theorem of A. Bonami, S. Durand and G. Weiss, in which only the case α = ∞ is treated. These two properties, together with a careful study of the “phases” that give rise to a wavelet from the MRA, will allow us to prove that the space Wα, of α-localized wavelets, is arcwise connected with the topology of L2((1 + |x|2)α dx) (modulo homotopy classes). This last result is new even for the case α = ∞, as well as the considerations about the “homotopy degree” of a wavelet.
Clasificación UNESCO 121007 ; 120217
Palabras clave español Espacio de medida ; Topología algebraica ; Homotopía ; Ondículas
Código MathReviews MR1697527
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