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Fourier transformation is an invertible integral transformation that map [[piecewise continuous functions]] from one [[topological group]] to another such that the kernel of the transformation is a generator of the group.

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

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.