Results 241 to 250 of about 10,586,623 (271)
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1983
The author continues and extends his previous investigations [ibid. 35(1983)]. He proves e.g. that if \(\phi\) is entire function in \({\mathbb{C}}\), D is a domain in \({\mathbb{C}}^ n\), and \(f\in H(D)\), then \({\tilde \phi}=\phi \circ f\) is GM-holomorphic and L(\({\tilde \phi}\))\(=\phi '\circ f\).
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The author continues and extends his previous investigations [ibid. 35(1983)]. He proves e.g. that if \(\phi\) is entire function in \({\mathbb{C}}\), D is a domain in \({\mathbb{C}}^ n\), and \(f\in H(D)\), then \({\tilde \phi}=\phi \circ f\) is GM-holomorphic and L(\({\tilde \phi}\))\(=\phi '\circ f\).
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WEAKLY HOLOMORPHIC FUNCTIONS ON COMPLETE INTERSECTIONS, AND THEIR HOLOMORPHIC EXTENSION
Mathematics of the USSR-Sbornik, 1988See the review in Zbl 0631.32009.
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On universal holomorphic functions
1988Let \(\{c_ n\}\) be a sequence in the complex plane C with lim \(c_ n=\infty\). \textit{W. Luh} [Colloq. Math. Soc. János Bolyai 19, 503-511 (1978; Zbl 0411.30017)] proved the existence of an entire function F such that, for every compact set \(K\subset C\) with connected complement, and for every function f(z) that is holomorphic in the interior of K ...
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2011
Abstract This chapter reviews some examples of holomorphic functions in complex analysis. It emphasizes the idea of ‘analytic continuation’, which is a fundamental motivation for Riemann surface theory.
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Abstract This chapter reviews some examples of holomorphic functions in complex analysis. It emphasizes the idea of ‘analytic continuation’, which is a fundamental motivation for Riemann surface theory.
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Spherical Monopoles and Holomorphic Functions
Bulletin of the London Mathematical Society, 2001In a monopole \((\nabla,\Phi)\) the curvature \(F_\nabla\) and the covariant derivative of the section \(\Phi\) are related by a nonlinear first-order partial differential equation \(F_\nabla= *d_\nabla\Phi\), where \(*\) is the Hodge star [see \textit{M. F. Atiyah, N. J. Hitchin} and \textit{I. M. Singer}, Proc. R. Soc. Lond., Ser.
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The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function
, 2016B. Khabibullin, T. Baiguskarov
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Normality Criteria of Meromorphic Functions Sharing a Holomorphic Function
, 2015D. Meng, P. Hu
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1992
Abstract Complex analysis may be summarized as the study of holomorphic functions. Holomorphic means—almost—the same as differentiable, but there is a critical distinction between the two concepts. This comes from the role played by open sets. h has different limiting values when h approaches O from different directions.
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Abstract Complex analysis may be summarized as the study of holomorphic functions. Holomorphic means—almost—the same as differentiable, but there is a critical distinction between the two concepts. This comes from the role played by open sets. h has different limiting values when h approaches O from different directions.
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Holomorphic Function Theory in Several Variables
, 2011Christine Laurent-Thiébaut
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Algebras of Holomorphic Functions
Proceedings of the London Mathematical Society, 1957openaire +1 more source