# inner function

## inner function

[¦in·ər ′fəŋk·shən]
(mathematics)
A continuous open mapping of a topological space X into a topological space Y where the inverse image of each point in Y is zero dimensional.
References in periodicals archive ?
'It is very good for the inner function of our system.
Let [H.sub.r,[theta]] (T) denote the set of all bounded and analytic functions in [T.sub.+] that can be represented as the product of a rational outer function r and an inner function [theta]
For the case when [phi] [member of] [H.sub.r,[theta]] (T), we designed the generalized factorization algorithm [AFact] (see  and ) that computes a left generalized factorization of factorable essentially bounded matrix functions of class (5.1), for any general inner function [theta].
Note that the computations of the [AFact] algorithm do not depend on the degree of the polynomials that may eventually be part of inner function [theta].
An inner function is an analytic function [phi] in D with [absolute value of [phi](z)] [less than or equal to] 1 and [absolute value of [phi]([e.sup.i[theta]])] = 1 for almost all [theta] (cf.
If [phi] is an inner function with [phi](0) = 0, then f(z) = [[summation].sup.p.sub.k=1] [[absolute value of z].sup.2(k-1)][G.sub.p-k+1]([phi](z)) [member of] EHs(F).
Then [[parallel]f[parallel].sub.2] = [[parallel]F[parallel].sub.2] if and only if there is some inner function [phi] with [phi](0) = 0 such that
The inner function 'F(u)' in the form '[phi]u' states that:
First, the truth-value of the logical product of the inner and outer functions is equal to the truth-value of the function that is constituted so that the argument of the inner function has the outer function as an attribute.
But there is no doubt of his deep love for modern dance, which he views as allowing dancers to express themselves in movement, or, as he puts it, "to balance inner function, thought, and feeling with outer form."
Let us observe that the above problem is similar to the construction of the inner function (see [1,13,14,15]).
Aleksandrov: Existence of inner function in the unit ball.Math.
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