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Functions holomorphic along holomorphic vector fields [PDF]
Journal of Geometric Analysis, 2008 The main result of the paper is the following generalization of Forelli's theorem: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues whose ratios are ...
B.V. Shabat +7 more
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Leafwise Holomorphic Functions [PDF]
Proceedings of the American Mathematical Society, 2001 It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the ...
Feres, R., Zeghib, A.
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Holomorphic Cliffordian functions [PDF]
Advances in Applied Clifford Algebras, 1998 The aim of this paper is to put the fundations of a new theory of functions, called holomorphic Cliffordian, which should play an essential role in the generalization of holomorphic functions to higher dimensions. Let R\_{0,2m+1} be the Clifford algebra of R^{2m+1} with a quadratic form of negative signature, D = \sum\_{j=0}^{2m+1} e\_j {\partial\over \
Laville, Guy, Ramadanoff, Ivan
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AxiomsScators form a linear space equipped with a specific non-distributive product. In the elliptic case they can be interpreted as a kind of hypercomplex number.
Jan L. Cieśliński +2 more
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Holomorphic Continuation of Functions Along a Fixed Direction (Survey)
Современная математика: Фундаментальные направления, 2022 In this article, we give an overview of the most significant and important results on holomorphic extensions of functions along a fixed direction. We discuss the following geometric questions of multidimensional complex analysis: • holomorphic extension ...
A. S. Sadullaev
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On local invertibility of functions of an h-complex variable
Журнал Белорусского государственного университета: Математика, информатика, 2022 The theory of functions of an h-complex variable is an alternative to the usual theory of functions of a complex variable, obtained by replacing the rules of multiplication.
Vladislav A. Pavlovsky, Igor L. Vasiliev
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Characterizations of Integral Type for Weighted Classes of Analytic Banach Function Spaces
Journal of Mathematics, 2022 The aim of this study is to give some new definitions of Banach spaces of holomorphic functions. Some holomorphic characterizations of integral type for some classes of Banach spaces of holomorphic functions are established in the unit disc U.
Amnah E. Shammaky, A. El-Sayed Ahmed
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Majorization Results for Certain Subfamilies of Analytic Functions
Journal of Function Spaces, 2021 Let h1z and h2z be two nonvanishing holomorphic functions in the open unit disc with h10=h20=1. For some holomorphic function qz, we consider the class consisting of normalized holomorphic functions f whose ratios fz/zqz and qz are subordinate to h1z and
Muhammad Arif +4 more
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Математичні Студії, 2022 Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{
V.P. Baksa, A. I. Bandura, T.M. Salo
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Classification of Holomorphic Functions as Pólya Vector Fields via Differential Geometry
Mathematics, 2021 We review Pólya vector fields associated to holomorphic functions as an important pedagogical tool for making the complex integral understandable to the students, briefly mentioning its use in other dimensions.
Lucian-Miti Ionescu +2 more
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