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Fourier transformation is an invertible integral transformation that decompose a [[piecewise continuous functions]] on a [[topological group]] into a linear combination of basis functions.

Fourier transformation is an invertible integral transformation that decompose a [[piecewise continuous functions]] on a [[topological group]] into a linear combination of basis elements.

Often, functions which are difficult to analyze in one topological group become much easier to analyze when transformed to another topological group.

Often, functions which are difficult to analyze in one topological group become much easier to analyze when transformed to another topological group.