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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Keywords: Holomorphic function, subharmonic function, Hausdorff measure, exceptional sets.
is said to admit a holomorphic extension if there exists [delta] > 0 and a holomorphic function [?
1] is a highly oscillatory integral, but its integrand is a holomorphic function.
In the next proposition, we study the continuity of the operator of multiplication by a holomorphic function.
Let f be a holomorphic function on X such that Sing(X) [subset] A = {f = 0}.
N] where every holomorphic function of N complex variables attains its maximum modulus, is contained in [([partial derivative]K).
Since the integrand extends to a holomorphic function that exhibits Gaussian decay along the direction of the real axis, we can shift the line of integration from R to R - i x/(2n+1)[sigma] and obtain
G(x/t, t) is a holomorphic function of t in some annulus about t = 0.
The latter has the property that the maximum modulus of any holomorphic function defined on a domain is attained at the Shilov boundary.
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.
He shows that the measure is the product of the squared modulus of a holomorphic function with the determinant of the imaginary part of the period matrix to the power of 13.

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