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  • Abstract Harmonic Analysis
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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.


Mahmoud Filali

Pekka Salmi

Tero Vedenjuoksu    

Tomi Alaste

Juho Rautio

Juho Rosqvist

Possible PhD-supervisors

Mahmoud Filali

Pekka Salmi (especially topics related to locally compact quantum groups)


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