inner function

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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Among the topics are tight and full spark Chebyshev frames with real entries and worst-case coherence analysis, spectral properties of an operator polynomial with coefficients in a Banach algebra, the invertibility of graph translation and support of Laplacian Fiedler vectors, p-Riesz bases in quasi-shift invariant spaces, and a matrix characterization of boundary representation of positive matrices in the Hardy space. ([umlaut] Ringgold, Inc., Portland, OR)
It is well-known that H[mathematical expression not reproducible], where [H.sup.q] (U) denotes the Hardy space on U.
Motivated by [17, 20, 37], etc, in this paper, we use the area integral function SL associated with the operator L to define the Herz-type Hardy space [H[??].sup.[alpha],p.sub.q,L]([R.sup.n]).
The Hardy space [H.sup.p], 1 [less than or equal to] p < [infinity], consists of those functions f in H(D) for which [mathematical expression not reproducible] where dm is the normalized arc length measure on T, where T = {z [member of] C : |z| = 1}.
The rearrangement- invariant Hardy space associated with x, [H.sub.x], consists of those f [member of] S'(R)/P such that
Recently, Ky [20] introduced a new Musielak-Orlicz Hardy space [H.sup.[phi]]([R.sup.n]), via the grand maximal function, and established its atomic characterization.
Ueki, "Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball," Applied Mathematics and Computation, vol.
Given a Schwartz function [phi] [member of] S([R.sup.d]) with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and supp [phi] [subset] [[0, 1/2].sup.d], the local Hardy space [h.sub.p]([R.sup.d]) (0 < p [less than or equal to] [infinity]) consists of all tempered distributions f for which
They are everywhere defined in some special cases on the classical Hardy Space [H.sup.2] (the case when [[beta].sub.n] = 1 for all n).
For p [member of][1, [infinity]) the Hardy space [H.sup.p]([[PI].sub.+]) consists of all f [member of] H([[PI].sub.+]) such that
An elementary inquiry, based on examples and counterexamples, of some qualitative properties of doubly orthogonal systems of analytic functions on domains in [C.sup.n] leads to a better understanding of the deviation from the classical Hardy space of the disk setting.
For instance the classical theorem of Beurling [3] on the structure of analytically invariant subspaces of the Hardy space on the torus has been influential in many areas of modern mathematics, ranging from the dilation theory of a contraction, to interpolation problems in function theory or to the probabilistic analysis of time series.