Theory of Fourier

In Analysis, the theory of Fourier gathers a whole of methods concerned with the application of the theory of the spaces of separable Hilbert S to the analyzes functional spaces L ². They aim at setting up transformations making it possible in an abstract way to bring back derivation to calculations on polynomials. One usually distinguishes:

the Fourier series: it is of encoder the functions (for example real) of a real variable periodicals and about integrable square by continuations of realities of summable square. This encoding is related to the density of the trigonometrical polynomials. The physicists speak about discrete Théorie of Fourier.
the Transformed of Fourier: it is about a transformation on the functions of a real and integrable variable or integrable square. The physicists speak about Théorie of Fourier continues.
the theory of Fourier for the finished groups.
the theory of Fourier for the topological groups locally compact.

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