abstract harmonic analysis

noun

A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.

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Meanings

nounabstract harmonic analysis (uncountable)
  1. uncountableharmonic analysis; representation theory; harmonic analysis; representation theorymathematicsA branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.

    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
    1 more example

    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.

Translations

Finnish abstrakti harmoninen analyysi
  • abstrakti harmoninen analyysibranch of harmonic analysis
Italian analisi armonica astratta
  • analisi armonica astrattabranch of harmonic analysis
Polish abstrakcyjna analiza harmoniczna
  • abstrakcyjna analiza harmonicznabranch of harmonic analysis
Cite this entry
APA

abstract harmonic analysis. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/abstract%20harmonic%20analysis

MLA

“abstract harmonic analysis.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/abstract%20harmonic%20analysis. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “abstract harmonic analysis,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/abstract%20harmonic%20analysis.

Source: abstract harmonic analysis on Wiktionary, CC BY-SA 4.0.