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Holomorphic Almost-Periodic Functions
Acta Applicandae Mathematica, 2001This is a survey paper concerning results on holomorphic almost-periodic functions and mappings in one and several complex variables, up today, with special attention payed to the achievements of the Kharkov school. There are presented results concerning almost-periodic distributions and currents, a.p. holomorphic chains and divisors, extension of a.p.
Favorov, S. Yu., Rashkovskii, A. Yu.
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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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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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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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Holomorphic harmonic functions
Russian Journal of Mathematical Physics, 2008We consider boundary problems for holomorphic harmonic functions on hyperboloids at ℂn using concepts of integral geometry.
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Interpolating Holomorphic Functions
2018One of the main results of this text is that the monodromy M(λ) can be reconstructed uniquely (up to a sign in the off-diagonal entries) from the spectral data \((\varSigma ,\mathcal {D})\).
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