# holomorphic function

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Related to holomorphic function: Meromorphic function

## 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 , Zhu proved that a holomorphic function belongs to Bloch space if and only if it is hyperbolic Lipschitz.
[??]([epsilon], z) is the 1-Gevrey asymptotic expansion as e tends to 0 of a holomorphic function f([epsilon], z) in S([theta], [gamma]; E) x [D.sub.r]; (c) if [gamma] > [pi] is chosen so that (4) holds, then the formal series [??]([epsilon], z) is, by an analogue of Borel-Ritt's theorem for Gevrey asymptotic expansion (see, e.g., Section 3.2 of ), 1-summable in the direction d and its sum equals f([epsilon], z).
Moreover the Hamiltonian is a holomorphic function at a neighborhood of the origin(equilibrium); the linear part of the first-order ordinary form of (35) coincides with
Keywords: Holomorphic function, subharmonic function, Hausdorff measure, exceptional sets.
Consider the holomorphic function F(z) := [??](z) - z defined on [B.sub.[delta]].
a rectangle) is conformally mapped onto another regular region, then this mapping is performed by a holomorphic function. This mapping is fully determined by its values on an arbitrarily small open subset of the region.
where F is a holomorphic function from R x [R.sup.n] into [R.sup.n], for n [greater than or equal to] 1.
Let f be a holomorphic function on X such that Sing(X) [subset] A = {f = 0}.
We recall that a Pick function is a holomorphic function [phi] in the upper half-plane H with [??][phi](z) [greater than or equal to] 0 for z [member of] H Pick functions are extended by reflection to holomorphic functions in C\R and they have the following integral representation
G(x/t, t) is a holomorphic function of t in some annulus about t = 0.
The major part of realization theory concerns the identification of a given holomorphic function as a transfer (characteristic) function of a system (colligation) or a linear fractional transformation of such a function.
We define a holomorphic function [sub.x3,18] on [[unknown character].sub.3] as

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