# harmonic analysis

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## harmonic analysis

n.
The study of functions given by a Fourier series or analogous representations, such as periodic functions and functions on topological groups.

## harmonic analysis

n
1. (Mathematics) the representation of a periodic function by means of the summation and integration of simple trigonometric functions
2. (Mathematics) the study of this means of representation

## harmon′ic anal′ysis

n.
the calculation or study of Fourier series and their generalization.
[1865–70]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 harmonic analysis - analysis of a periodic function into a sum of simple sinusoidal componentsFourier analysisanalysis - a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
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However, one limitation of the Fourier theory is its accuracy, which is deficient for extreme low-temperature or ultra-short-pulse thermal heating in temporal-spatial scale [3-6].
The text covers sets and functions, Lebesgue measure, measurable sets, Borel sets, sets of measure zero, the integral, measurable functions, convergence theorems, convergence in mean, Fourier theory, calculus, change of variables, differentiation of integrals, integration of derivatives, and general measures.
In the Fourier transform literature, the Heisenberg Uncertainty Principle is derived from a general theorem of Fourier theory called the Uncertainty Theorem [7].

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