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harmonic analysis

Study of superpositions in mathematics

Instance of: branch of mathematics
Subclass of: data analysis
Part of: advanced mathematics
, mathematical analysis

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

Harmonic analysis is an area of mathematical analysis that emerged from the study of harmonic functions, and especially their boundary behavior. The methods of harmonic analysis decompose functions and related objects, such as measures, into components based on symmetries, scales, spectra, or oscillation. It is also concerned with the analytic estimates for operators arising from such decompositions. Basic examples include Fourier series and the Fourier transform, while modern harmonic analysis also studies maximal functions, singular integrals, oscillatory integrals, Fourier multipliers, Littlewood–Paley theory, and spectral decompositions.

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34 statements · 38% with external sources · numbers in brackets are citations

Different from: Spectral analysis

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29 identifiers linking harmonic analysis across the web's reference databases

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statements

38%

externally sourced

Source last edited June 11, 2026. AIDB refreshes this page daily.

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AIDB. (2026). harmonic analysis (Q876215). Retrieved from https://aidb.si/e/harmonic-analysis-Q876215