Multidimensional wavelets in non-isotropic function spaces

University Of Oregon Eugene, Eugene OR

Investigators

Abstract

The project involves education and research activities in harmonic analysis concerning the mathematical theory of multi-dimensional wavelet expansions. One of the fundamental problems of the subject is how to construct wavelets with desired properties such as good time-frequency localization. Despite significant progress in this area, the majority of research has been concentrated on isotropic theory and non-isotropic wavelet theory lags far behind. One of the main research directions of the project is the development of techniques for construction of well-localized orthogonal wavelets for large classes of non-isotropic expansive dilations. A closely related complementary topic is the identification of non-isotropic dilations for which the construction of well-localized wavelets is not possible. Another direction of the project is to study non-isotropic analogues of classical function spaces associated to expansive dilations. More generally, the project represents work on wavelet analysis which is a powerful technique in harmonic analysis. Non-isotropic wavelet theory in higher dimensions has a potential for wide applications both in pure analysis and more applied areas of signal and image processing comparable to that of already well established isotropic wavelet theory. The main goal of the project is to integrate research and education activities in the multidimensional wavelet theory which could make further applications of non-isotropic wavelets possible.