abstract harmonic analysis

abstract harmonic analysis (uncountable)

1. (harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological 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 of abstract 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 on abstract harmonic analysis and its applications.

   • 2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis‎, 2nd edition, Taylor & Francis (CRC Press):

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