Results 131 to 140 of about 5,162,686 (175)
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Coefficients of Holomorphic Functions
Journal of Mathematical Sciences, 2001Denote by \(S\) the class of holomorphic univalent functions \(f\) in the disc \(E=\{z\in \mathbb{C}:|z|< 1\}\) of the form \[ f(z)= z+\sum^\infty_{n=2} a_n z^n \] and by \(S(M)\), and \(M> 1\), the subclasses of \(S\) of functions \(f\) satisfying the condition \(|f(z)|< M\) for \(z\in E\).
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Kuratowski Convergence of Holomorphic Functions
Monatshefte f�r Mathematik, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferrera, Juan, Prieto, Ángeles
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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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Kergin Interpolants of Holomorphic Functions
Constructive Approximation, 1997Let \(D\subset\mathbb{C}^n\) be a \(\mathbb{C}\)-convex domain, that is, its intersection with each complex line \(\ell\) is a simply connected domain in \(\ell\). Let \(\{a_{nm}\}\), \(n= 1,2,\dots\), \(m= 1,2,\dots, n\) be an array of points in a compact set \(K\subset D\). Then, it is shown that for a function \(f\) holomorphic in \(D\) there exists
Bloom, T., Calvi, J.-P.
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Separating Singularities of Holomorphic Functions
Canadian Mathematical Bulletin, 1998AbstractWe present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for other classes of functions.
Müller, Jürgen, Wengenroth, Jochen
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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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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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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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