Session S05 - Advances on Spaces of Non-absolutely Integrable Functions and Related Applications

Monday, July 12, 13:45 ~ 14:15 UTC-3

Haar, Wavelets System, Multi-Resolutions and The special atom space in Higher Dimensions and its Analytic Characterizations

Geraldo De Souza

Auburn University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this presentation, we will explore the special atom spaces introduced by De Souza in 1980 in his Ph.D thesis. The impetus of this exploration to extend to higher dimension the definition originally proposed by De Souza. This leads to a natural “new” definitions of Haar System and Wavelets in Higher dimensions, even though these definitions has been discussed by numerous authors in the literature, the definitions proposed do not always seems natural extension of one dimensions case and often are unnecessarily cumbersome and difficulty to follows. Also, we explore the analytic characterizations of these special atom spaces in Higher Dimensions, which answer a question proposed by Brett Wick on the spaces of certain analytic functions spaces in the bidisc. We also have some applications of Haar-Wavelets and a Multi-resolution analysis in 2-dimensions

Joint work with Eddy Kwessi (Trinity University, USA).

View abstract PDF