Representative function

Representative function

In mathematics, in particular in the field of the representation theory of groups, a representative function is a function "f" on a compact topological group "G" obtained by composing a representation of "G" on a vector space "V" with a linear map from the endomorphisms of "V" into "V" 's underlying field. Representative functions arise naturally from finite-dimensional representations of "G" as the matrix-entry functions of the corresponding matrix representations.

It follows from the Peter-Weyl theorem that the representative functions on "G" are dense in the Hilbert space of square-integrable functions on "G".

References

* Theodor Bröcker and Tammo tom Dieck, "Representations of compact Lie groups", Graduate Texts in Mathematics 98, Springer-Verlag, Berlin, 1995.


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • representative — A person or thing that represents, or stands for, a number or class of persons or things, or that in some way corresponds to, stands for, replaces, or is equivalent to, another person or thing. Gaffney v. Unit Crane & Shovel Corp., D.C.Pa., 117 F …   Black's law dictionary

  • Representative town meeting — A representative town meeting is a form of municipal legislature particularly common in Massachusetts, New Hampshire, Connecticut and Vermont.Representative Town Meetings function largely the same as an Open Town Meeting, except that not all… …   Wikipedia

  • Representative sequences — Protein sequences can provide data about the biological function and evolution of proteins and protein domains. Grouping and interrelating protein sequences can therefore provide information about both human biological processes, and the… …   Wikipedia

  • Rational function — In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. DefinitionsIn the case of one variable, x , a rational function is a function of the form: f(x) = frac{P(x)}{Q(x)}where P and Q are …   Wikipedia

  • High Representative for the Common Foreign and Security Policy — The High Representative for the Common Foreign and Security Policy (HR) is the main co ordinator of the Common Foreign and Security Policy within the European Union. The position is currently held by Javier Solana and is based in the General… …   Wikipedia

  • Consul (representative) — Consulate and honorary consul redirect here. For the Graham Greene novel, see The Honorary Consul. For the uses of consul as the chief magistrate of a city state, see Consul. The political title Consul is used for the official representatives of… …   Wikipedia

  • Likelihood function — In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of …   Wikipedia

  • People's Representative Council — Dewan Perwakilan Rakyat …   Wikipedia

  • Zeta function universality — In mathematics, the universality of zeta functions is the remarkable property of the Riemann zeta function and other, similar, functions, such as the Dirichlet L functions, to approximate arbitrary non vanishing holomorphic functions arbitrarily… …   Wikipedia

  • Polynomial and rational function modeling — In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.Polynomial function modelsA polynomial function is one that has the form:y = a… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”