Theory of Functions Research Group

Members:

UAB: Gerard Ascensi, Josep M. Burgués, Joan J. Carmona, Julià Cufí, Joan J. Donaire, Joaquim Martin, Margarida Miró.
UB: Carme Cascante, Konstantin Dyakonov, Joan Fàbrega, Jordi Marzo, Xavier Massaneda, Joaquin M. Ortega, Joaquim Ortega-Cerdà, Daniel Pascuas.

Goals:

The UAB/UB Theory of Functions Group mainly develops its own lines of research on harmonic analysis, potential theory, conformal geometry and single- and multi-variable complex analysis. The group tries to provide a single, consolidated vision of these areas of mathematical analysis, emphasising how they are related to each other, in terms of both technique and content, within the overall context of the theory of functions. The primary focus of the research group is the relationship between the metric, topological and geometric properties of sets and the power of the theory of functions that they support. Specific aspects include sets of avoidable singularities for different types of functions, sets of uniqueness or determinants for different types of analytic functions and their relationship with sampling problems in signal processing, exceptional sets in conformal representation theory and their relationship with the study of the properties of harmonic measure, the fine regularity properties of associated potentials and capacities, self-similar and fractal sets and their Hausdorff dimensions, etc.

Keywords

Holomorphic functions, Cauchy-Riemann equations, conformal representation, quasi-conformal applications, probability methods, sampling and interpolation, geometric theory of functions, signal analysis, time and frequency analysis, wavelet theory.