Results 21 to 30 of about 15,024,563 (297)
An independence result in several complex variables [PDF]
Proceedings of the American Mathematical Society, 1991 The assertion that there exists a complete set of biholomorphic invariants for simply connected domains in C
Lempert, László, Rubel, Lee A.
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Kernel convergence and biholomorphic mappings in several complex variables
International Journal of Mathematics and Mathematical Sciences, 2003 We deal with kernel convergence of domains in ℂn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem,
Gabriela Kohr
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The *-product of domains in several complex variables
Complex Variables and Elliptic Equations, 2022 In this article we continue the research, carried out in \cite{zajac}, on computing the $*$-product of domains in $\CC^N$. Assuming that $0\in G\subset\CC^N$ is an arbitrary Runge domain and $0\in D\subset\CC^N$ is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between $D*G$ and ...
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One complex variable versus several complex variables: The Hartogs extension phenomenon in context [PDF]
Opuscula MathematicaWe explicate the difference between the function theory of one complex variable and the function theory of several complex variables. In particular, we use the inhomogeneous Cauchy-Riemann equations to explain why there is a Hartogs extension phenomenon ...
Steven G. Krantz
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On Pólya’s Theorem in several complex variables [PDF]
Banach Center Publications, 2015 Let $K$ be a compact set in $\mathbb{C}$, $f$ a function analytic in $\overline{\mathbb{C}}\smallsetminus K$ vanishing at $\infty $. Let $% f\left( z\right) =\sum_{k=0}^{\infty }a_{k}\ z^{-k-1}$ be its Taylor expansion at $\infty $, and $H_{s}\left( f\right) =\det \left( a_{k+l}\right) _{k,l=0}^{s}$ the sequence of Hankel determinants.
Günyüz, Ozan, Zakharyuta, Vyacheslav
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Representation of logarithm of entire function in several complex variables
Karpatsʹkì Matematičnì Publìkacìï, 2013 The integral representation of some branch of an entire on $\mathbb{C}^n$ function which generalized the Poisson-Jensen-Stoll Formula is obtained.
O. Ya. Brodyak, Ya. V. Vasyl'kiv
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A note on monomials in several complex variables [PDF]
Proceedings of the American Mathematical Society, 1974 Monomials in C'1 are characterized in the polydisk algebra A(Un) as functions whose modulus is constant on the distinguished boundary of U' and whose zero set has an intersection with the diagonal of U', consisting (at most) of the origin. The note answers a question raised by F.
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On Polyanalytic Functions in Several Complex Variables
Complex Analysis and Operator Theory, 2023 AbstractWe give a characterisation of the polyanalytic type subspaces of the Hilbert spaces $$\mathcal {H}$$ H , being the weighted $$L_2$$ L 2 function spaces on a connected simply connected domains $$D \subset \mathbb {C}^n$
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k-convexity in several complex variables [PDF]
Annales Polonici Mathematici, 2002 Formerly, D.~Mejia, D.~Minda and W.~Ma investigated the hyperbolic geometry of \(k\)-convex regions in \(\mathbb C\), \(k\)-convex functions on the unit disk \(U \in \mathbb C\), and obtained growth and distortion theorems for \(k\)-convex functions on \(U\). In this paper, their results are generalized for the case of several complex variables.
Hamada, Hidetaka, Kohr, Gabriela
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A Note on Strongly Starlike Mappings in Several Complex Variables
Abstract and Applied Analysis, 2014 Let f be a normalized biholomorphic mapping on the Euclidean unit ball 𝔹n in ℂn and let α∈0,1. In this paper, we will show that if f is strongly starlike of order α in the sense of Liczberski and Starkov, then it is also strongly starlike of order α in ...
Hidetaka Hamada +3 more
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