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# Rademacher system

In mathematics, in particular in functional analysis, the Rademacher system, named after Hans Rademacher, is an incomplete orthogonal system of functions on the unit interval of the following form:

\( \{ t \mapsto r_{n}(t)=\sgn ( \sin 2^{n+1} \pi t ) ; t \in [0,1], n \in \N \}. \)

The Rademacher system is stochastically-independent, and is closely related to the Walsh system. Specifically, the Walsh system can be constructed as a product of Rademacher functions.

References

"Orthogonal system". Encyclopaedia of Mathematics.

Heil, Christopher E. (1997). "A basis theory primer" (PDF).

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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