abstract harmonic analysis
noun1
Mathematics, Sciences, Topology A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.
Harmonic analysis; representation theory; harmonic analysis; representation theory
- 1970, Edwin Hewitt, Kenneth A. Ross, Abstract Harmonic Analysis: Volume II: Structure and Analysis for Compact Groups; Analysis on Locally Compact Abelian Groups, Springer, 2nd reprint, 2002, page 547, WIENER [1] goes well beyond analysis of periodic functions on R or even functions in 𝔏₂(R); this important paper has yet to be interpreted and assimilated into the standard repertory of abstract harmonic analysis.
- The present book is a text book for a graduate course on abstract harmonic analysis and its applications.2014, Anton Deitmar, Siegfried Echterhoff, Principles of Harmonic Analysis, 2nd edition, Springer, page v: