abstractharmonicanalysis (uncountable)

1. (harmonic analysis, representation theory, topology) A branch ofharmonic analysis dealing with generalisedFourier transforms that act onfunctions defined onHausdorfflocally compacttopological groups.
   • 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${\displaystyle R}$ or even functions in${\displaystyle {\mathfrak{L}}_2(R)}$; this important paper has yet to be interpreted and assimilated into the standard repertory ofabstract harmonic analysis.

   • 2014, Anton Deitmar, Siegfried Echterhoff,Principles of Harmonic Analysis, 2nd edition, Springer,page v:

     The present book is a text book for a graduate course onabstract harmonic analysis and its applications.

   • 2015, Gerald B. Folland,A Course inAbstract Harmonic Analysis‎^[1], 2nd edition, Taylor & Francis (CRC Press):

• Harmonic analysis on Wikipedia.Wikipedia
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  • Pontryagin duality on Wikipedia.Wikipedia
• Harmonic analysis, abstract onEncyclopedia of Mathematics
• Fourier transform onEncyclopedia of Mathematics

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