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 |
Acceso al artículo completo |