Parry point (triangle): Difference between revisions
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In mathematics, in particular in [[functional analysis]], the '''Rademacher system''', named after [[Hans Rademacher]], is an [[Complete orthogonal system # Incomplete orthogonal sets|incomplete orthogonal system]] of functions on the [[unit interval]] of the following form: | |||
: <math>\{ t \mapsto r_{n}(t)=\sgn ( \sin 2^{n+1} \pi t ) ; t \in [0,1], n \in \N \}.</math> | |||
The Rademacher system is stochastically-independent, and is closely related to the [[Walsh transform|Walsh]] system. Specifically, the [[Walsh transform|Walsh system]] can be constructed as a product of Rademacher functions. | |||
==References== | |||
* {{Cite web| url=http://eom.springer.de/O/o070380.htm |title=Orthogonal system |work=Encyclopaedia of Mathematics }} | |||
* {{Cite web| last=Heil | first=Christopher E. | title=A basis theory primer | url=http://www.math.gatech.edu/~heil/papers/bases.pdf | format=PDF | date=1997 }} | |||
[[Category:Functional analysis]] | |||
{{Mathanalysis-stub}} | |||
Revision as of 07:41, 23 January 2014
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:
![{\displaystyle \{t\mapsto r_{n}(t)=\operatorname {sgn}(\sin 2^{n+1}\pi t);t\in [0,1],n\in \mathbb {N} \}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8fda4ec4f39c9ac27c324a11950d1f8f547e98f)
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.