Results 1 to 10 of about 210 (150)
Analytic continuation of holomorphic functions with values in a locally convex space [PDF]
Proceedings of the American Mathematical Society, 1969 Horvath [3] has announced a result generalizing the result of Gelfand and Shilov [2] on analytic continuation of holomorphic functions with values in a locally convex space. In this paper we shall present a generalization of these results which permits one to prove the existence of strong holomorphic extensions from the existence of weak or weak ...
Witold M. Bogdanowicz
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Holomorphic extension of continuous, weakly holomorphic functions on certain analytic varieties [PDF]
Nagoya Mathematical Journal, 1973 Let M, N be connected complex submanifolds of a neighborhood of the origin 0 ∈ Cd, the space of d complex variables, such that 0 ∈ M ∩ N. We shall suppose throughout that M ⊄ N and N ⊄ M in any neighborhood of 0. Let X = M ∪ N. X is an analytic subvariety with the irreducible branches M and N. Let Δ be a neighborhood of 0 in Cd.
Nozomu Mochizuki
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Generalized analytic functions, Moutard-type transforms, and holomorphic maps [PDF]
Functional Analysis and Its Applications, 2016 We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with ...
P. G. Grinevich, Roman Novikov
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Analytic families of holomorphic iterated function systems [PDF]
Nonlinearity, 2008 30 pages, the title is changed.
Mario Roy +2 more
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An extension theorem for separately holomorphic functions with analytic singularities [PDF]
Annales Polonici Mathematici, 2003 Let \(D_j\subset\mathbb{C}^{k_j}\) be a pseudoconvex domain and \(A_j \subset D_j\) be a locally pluriregular set, \(j=1,\dots,N\), \(N\geq 2\). Put \[ X:= \bigcup^N_{j=1} A_1\times\cdots \times A_{j-1}\times D_j\times A_{j+1}\times \cdots\times A_N. \] The main result of this paper is the following. Theorem. Let \(U\) be an open connected neighborhood
Marek Jarnicki, Peter Pflug
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Extension of holomorphic functions through a hypersurface by tangent analytic discs [PDF]
Hokkaido Mathematical Journal, 2003 Let \(\Omega\) be a domain in \(\mathbb{C}^n\) with boundary \(M\), and \(A\) an analytic disc attached to \(\overline\Omega\) and not to \(M\), i.e., \(\partial A\subset\overline\Omega\) but \(\partial A\not\subset M\). Assume \(A\) is tangent to \(M\) at a point \(z^0\in\partial A\cap M\). The author proves that if \(B\) is a ball with center \(z^0\)
Giuseppe Zampieri
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On some properties of p-holomorphic and p-analytic function
Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2021 In this article the relationship between the conditions of p-differentiability, p-holomorphycity, and the existence of the derivative of a function of a p-complex variable is considered. The general form of a p-holomorphic function is found. The sufficient conditions for p-analyticity and local invertibility are obtained.
I. L. Vassilyev, V. V. Dovgodilin
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General Integral Representation of the Holomorphic Functions on the Analytic Subvariety
Publications of the Research Institute for Mathematical Sciences, 1993 A compact metric space \(R\) is called a slit space if there is a nonempty closed subset (slit) \(S \subset R\), s.t. each point of it is an accumulation point for \(R \setminus S\), and \(R \setminus S\) is homeomorphic to a topological product of a connected differential manifold of class \(C^ 2\) and a compact set.
Shu Jin Chen
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Some Conclusions on Holomorphic Function and Analytic Function
DEStech Transactions on Social Science, Education and Human Science, 2017 In many applied sciences, such as physics, engineering, etc. the holomorphic function plays an extremely important role, and at the same time, the analytic function plays an extremely important role. In this article, we tries to clarify, under certain conditions, they are the same kind of function. We will see that a function is analytic if and only if
Lijiang Zeng
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$C\sp{k}$, weakly holomorphic functions on analytic sets [PDF]
Proceedings of the American Mathematical Society, 1973 Let V be a complex analytic set and p e V. Let ((V), ((V), and Ck(V) denote respectively the rings of germs of holomorphic, weakly holomorphic, and k-times continuously differentiable functions on V. Spallek proved that there exists sufficiently large k such that Ck(V)r)((V)=C(V).
Joseph Becker
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