holomorphic function

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holomorphic function

[¦häl·ō¦mȯr·fik ′fəŋk·shən]
(mathematics)
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1) define holomorphic functions with respect to t near a movable singularity [t.
Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer- Verlag, New York, 2005.
3] in terms of their Gauss maps and auxiliary holomorphic functions (see [12]).
q] denote holomorphic functions C[[x]], or more generally, functions of the form
We shall estimate the growth of the holomorphic function
G(x/t, t) is a holomorphic function of t in some annulus about t = 0.
Examples cited of (seemingly) "magical" effects arising from holomorphic functions include:
We note that the general study of arbitrary conformal mappings between two spheres belongs historically to the realm of complex variables and holomorphic functions on the Riemann sphere (which is precisely the analytical equivalent of the complex plane augmented with a point at infinity (Kodaira 1984)).
Among the topics are arithmetic and topology in the complex plane, holomorphic functions and differential forms, isolated singularities of holomorphic functions, harmonic functions, the Riemann mapping theorem and Dirichlet's problem, and the complex Fourier transform.
He provides all the necessary prerequisites for graduate students and practitioners, describing Riemann surfaces (including coverings, analytical continuation, and Puiseaux expansion), holomorphic functions of several variables (including analytic sets and analytic set germs as well as regular and singular points of analytic sets), isolated singularities of holomorphic functions (including isolated critical points and the universal unfolding), fundamentals of differential topology (including singular homology groups and linking numbers), and the topology of singularities (including the Picard-Lefschetz theorem, the Milnor fibration, the Coxeter-Dynkin diagram, the Selfert form and the action of the braid group.
By the uniqueness theorem for holomorphic functions formula (2.
The opening paper describes the space of continuous functionals for a Smirnov space and defines the class of holomorphic functions representable by Carleman's formula.