harmonic analysis roots mid th century analysis topological groups core motivating ideas various fourier transforms generalized transform functions defined hausdorff locally compact topological groups theory abelian locally compact groups called pontryagin duality harmonic analysis studies properties duality fourier transform attempts extend features different settings instance case non abelian lie groups general non abelian locally compact groups harmonic analysis closely related theory unitary group representations compact groups
Formal science Mathematics Pure mathematics Analysis Harmonic analysis