holomorphic function

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hol·o·mor·phic function

(hŏl′ō-môr′fĭk, hō′lō-)
n. Mathematics
A function on a region of a complex plane, differentiable at every point in the region. Also called analytic function.
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In fact, consider a family of holomorphic functions [f.sub.j]:D [right arrow] [P.sup.2] defined as [f.sub.j](z) = (1;[[e.sup.-j]sup.2] - 1; [-e.sup.jz]) where D is the unit disk.
This overview of recent concepts and findings in large algebraic substructures is for advanced undergraduate and graduate students with background in calculus of real variables, Lebesgue integration, set theory, linear algebra, general topology, Hilbert/Banach spaces, complex variables, and holomorphic functions. Fortunately, each chapter starts with a brief list of necessary math required for understanding the chapter.
The function [phi] induces the composition operator [C.sub.[phi]], defined on the space of holomorphic functions on U by [C.sub.[phi]] f = f [omicron] [phi].
Let {[f.sub.n]} be a sequence of meromorphic functions in D, and let {[[psi].sub.n]} be a sequence of holomorphic functions in D such that [[psi].sub.n] [??] [psi], where [psi](z) [not equal to] 0, [infinity] in D.
They begin with the more elementary separately holomorphic functions without singularities, then move into the situation of existing singularities.
STESSIN, On n-widths of classes of holomorphic functions with reproducing kernels, Illinois J.
In this paper, by using the Bergman geometry, properties of holomorphic functions and related analyses, we characterize the conjugate holomorphic symbols for which the corresponding iterated commutators are bounded, compact or in the Schatten p-class.
For -[infinity] < [alpha] < [infinity], [[beta].sub.log[alpha]] denotes the weighted Bloch space consisting of holomorphic functions h in D satisfying
Euclidean Clifford analysis offers a function theory with the Dirac operator, which is an elegant generalization to higher dimensions of holomorphic functions in the complex plane.
(A) The theory of holomorphic functions of one complex variable is the central object of study in complex analysis.
where [OMEGA] is a simply-connected domain in C such that 0,1 [member of] [OMEGA] while [alpha][beta] [not member of] [OMEGA], O([OMEGA]) denotes the set of holomorphic functions on [OMEGA], and [H.sup.+.sub.[lambda]] = [H.sup.+.sub.[lambda]] (w, [[partial derivative].sub.w]) is the Heun ordinary differential operator given by