Inner functions and local shape of orthonormal wavelets

Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of L 2(ℝ)

“…Finally, that the function ψ given by (40) ±,j }-see Appendix A.2-is done in [6,7]. Here we release without proof some of the results obtained in these works.…”

“…Proof The result is a straightforward consequence of the change of representation formulas (6) and the fact that GDG −1 is the operator "multiplication by ω" on GL 2 (R) and F T F −1 is the operator "multiplication by ω" on F L 2 (R).…”

“…For wavelets with arbitrary support, several families of Hardy functions with intertwined orthonormality relations appear. See [6] for details.…”

“…At the same time, suitable choices of the bases lead to sparse sets of conditions (compare, for example, the matrices (α s,j,m i,n ) for the exponential and Haar bases in Appendix). A first analysis of this set of conditions for Haar bases is done in [6,7]. Section 6 releases some of the results obtained in these works.…”

Fórmulas y algoritmos espectrales para wavelets ortonormales y frames ajustados: aplicaciones en el procesamiento digital de imágen médica

“…Podemos encontrar una relación entre estos trabajos y el trabajo aquí desarrollado en [68]. Además, otras aplicaciones a la teoría de wavelets de las técnicas espectrales que aquí se presentan se describen en [67].…”