Abstract harmonic analysis is basically analysis on topological groups. Basic objects are functions and measures defined on groups and phenomena associated with these. Fourier analysis on locally compact abelian groups forms a beautiful theory, and this theory has been extended to several directions with variable success. Another common theme is to study Banach algebras of functions or measures. We consider abstract harmonic analysis to cover also objects associated to semigroups and to quantum groups. The research area combines group theory, Fourier analysis, functional analysis, theory of Banach algebras and operator algebras.
Pekka Salmi (especially topics related to locally compact quantum groups)
firstname.lastname (at) oulu.fi