Fernando Gómez-Cubillo

ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

Spectral decompositions of translation and dilation operators are built in terms of suitable orthonormal bases of L2(ℝ), leading to spectral formulas for scaling functions and orthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulas are useful to compute compactly supported scaling functions and wavelets. It is illustrated with a particular choice of the orthonormal bases, the so-called Haar bases, which yield a new algorithm related to the infinite product matrix representation of Daubechies and Lagarias.

Spectral models for orthonormal wavelets and related algorithms

This work presents new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces are in the core of the structure of these families. The new algorithms focus on the local shape of the wavelets, a property making them especially useful for pattern recognition.

SHORT RANGE POTENTIAL SCHRÖDINGER SCATTERING

We review certain general properties of short range potential scattering and discuss eigenfunction expansions related to short range and spherically symmetric potentials. In the case of a square barrier potential with a hard core at the origin, we study resonance phenomena and construct Gamow vectors in the radial representation.