Results 11 to 20 of about 28,571 (151)
Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables [PDF]
Symmetry, 2020 This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real
Renata Długosz, Piotr Liczberski
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Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables [PDF]
Symmetry, 2019 Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular domain of the
Edyta Trybucka
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Journal of the Korean Mathematical Society, 2016 Summary: In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables.
Cao, Tingbin, Liu, Zhixue
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Journal of Mathematical Analysis and Applications, 2001 Bohr's theorem [\textit{H. Bohr}, Proc. Lond. Math. Soc. (2) 13, 1-5 (1914; JFM 44.0289.01)] states that given an analytic function in the unit disk, \(f(z) = \sum_k c_k z^k\), such that \(|f(z)|< 1\) for any \(z\) in the disk, then \(\sum_k |c_k z^k|0\), and a compact set \(K\) such that \(\|f\|_U \leq C |f|_K\), for all bounded holomorphic \(f\).
Aizenberg, Lev +2 more
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Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Discrete Analysis, 2023 Bi-parameter potential theory and Carleson measures for the Dirichlet space on the bidisc, Discrete Analysis 2023:22, 58 pp. Carleson measures arise naturally when considering harmonic or holomorphic extensions from the boundary of a domain to the ...
Nicola Arcozzi +3 more
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Inequalities for holomorphic functions of several complex variables [PDF]
Transactions of the American Mathematical Society, 1983 Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and C n {{\mathbf {C}}^n} are established by using the notion of reproducing kernels.
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Asymptotic first boundary value problem for holomorphic functions of several complex variables [PDF]
Canadian Mathematical Bulletin, 2021 AbstractIn 1955, Lehto showed that, for every measurable function $\psi $ on the unit circle ${\mathbb T}$ , there is a function f holomorphic in the unit disc ${{\mathbb D}}$ , having $\psi $ as radial limit a.e. on ${\mathbb T}$ . We consider an analogous boundary value problem, where the unit disc is replaced by a Stein domain on a complex ...
Paul M. Gauthier, Mohammad Shirazi
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Bounded Holomorphic Functions of Several Complex Variables. I [PDF]
Transactions of the American Mathematical Society, 1971 A domain of bounded holomorphy in a complex analytic manifold is a maximal domain for which every bounded holomorphic function has a bounded analytic continuation. In this paper, we show that this is a local property: if, for each boundary point of a domain, there exists a bounded holomorphic function which cannot be continued to any neighborhood of ...
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Slice Holomorphic Functions in the Unit Ball Having a Bounded L-Index in Direction
Axioms, 2020 Let b∈Cn\{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e., we study functions that are analytic in the intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12 ...
Andriy Bandura +2 more
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Boundary Morera theorems for holomorphic functions of several complex variables
Duke Mathematical Journal, 1991 Sei \(D\subset\mathbb{C}^ N\) ein beschränktes Gebiet und \(A(D):=C(\overline D)\cap{\mathcal O}(D)\). In der Arbeit geht es um die Frage, wann eine Funktion \(f\in C(\partial D)\) nach \(D\) holomorph fortsetzbar, d.h. Beschränkung einer Funktion aus \(A(D)\) ist. Eine notwendige und unter geeigneten Voraussetzungen auch hinreichende Bedingung ist die
Globevnik, Josip, Stout, Edgar Lee
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