harmonic analysis


: the expression of a periodic function as a sum of sines and cosines and specifically by a Fourier series

Examples of harmonic analysis in a Sentence

Recent Examples on the Web Professor Tao has authored more than 300 research papers on an amazingly wide swath of mathematics including harmonic analysis, partial differential equations, combinatorics, number theory, data science, random matrices and much more. Quanta Magazine, 1 Feb. 2024 The conjecture turns out to have implications not only for geometry, but also for harmonic analysis and the study of partial differential equations. Quanta Magazine, 23 Dec. 2023 Croot introduced powerful new methods from harmonic analysis — a branch of math closely related to calculus — to confirm the Erdős-Graham prediction. Quanta Magazine, 9 Mar. 2022 After introducing new ideas in harmonic analysis and obtaining important results in an area called Calderón-Zygmund operator theory in the 1970s, Meyer wandered to the fledgling study of wavelets in the mid-1980s. Quanta Magazine, 21 Mar. 2017

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Word History

First Known Use

1867, in the meaning defined above

Time Traveler
The first known use of harmonic analysis was in 1867

Dictionary Entries Near harmonic analysis

Cite this Entry

“Harmonic analysis.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/harmonic%20analysis. Accessed 3 Mar. 2024.

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