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The main result of the paper is the following generalization of Forelli’s theorem (Math. Scand. 41:358–364, 1977): 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 eigenvalues whose ratios are positive reals. Then any function φ that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p.
We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.
K.T. Kim and G. Schmalz were supported by the Scientific visits to Korea program of the AAS and KOSEF. E. Poletsky was supported
by NSF Grant DMS-0500880. G. Schmalz gratefully acknowledges support and hospitality of the Max-Planck-Institut für Mathematik
Bonn. 相似文献
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Jasmin Raissy 《Journal of Geometric Analysis》2013,23(4):1993-2019
Let f 1,…,f h be h≥2 germs of biholomorphisms of ? n fixing the origin. We investigate the shape that a (formal) simultaneous linearization of the given germs can have, and we prove that if f 1,…,f h commute and their linear parts are almost simultaneously Jordanizable, then they are simultaneously formally linearizable. We next introduce a simultaneous Brjuno-type condition and prove that, in case the linear terms of the germs are diagonalizable, if the germs commute and our Brjuno-type condition holds, then they are holomorphically simultaneously linearizable. This answers a multi-dimensional version of a problem raised by Moser. 相似文献
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The aim of this paper is to put the foundations 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 ℝ0,2m+1 be the Clifford algebra of ℝ2m+1 with a quadratic form of negative signature, be the usual operator for monogenic functions and Δ the ordinary Laplacian. The holomorphic Cliffordian functions are functionsf: ℝ2m+2 → ℝ0,2m+1, which are solutions ofDδ
m
f = 0.
Here, we will study polynomial and singular solutions of this equation, we will obtain integral representation formulas and
deduce the analogous of the Taylor and Laurent expansions for holomorphic Cliffordian functions.
In a following paper, we will put the foundations of the Cliffordian elliptic function theory. 相似文献
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Holomorphic families of injections 总被引:5,自引:0,他引:5
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The present paper gives a survey of up-to-date results of holomorphic almost-periodic functions and mappings in one and several complex variables. 相似文献
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Let X = G/K be a Riemannian symmetric space of non-compact type. We prove a theorem of holomorphic extension for eigenfunctions of the
Laplace–Beltrami operator on X, by techniques from the theory of partial differential equations. 相似文献
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A. L. Pavlov 《Siberian Mathematical Journal》2016,57(5):860-865
We give necessary and sufficient conditions for a holomorphic factorization of an irreducible polynomial P(s, λ), s ∈ Cn, λ ∈ C, in a domain Ω ? Cn which is connected with the ordering of the real part of the roots of the equation P(s, λ) = 0, s ∈ Ω. 相似文献
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D. V. Prokhorov 《Journal of Mathematical Sciences》2001,106(6):3518-3544
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关于全纯函数的正规定则 总被引:5,自引:0,他引:5
张庆彩 《数学的实践与认识》2006,36(6):283-286
研究涉及微分多项式与公共值的全纯函数族的正规性问题.设F为区域D内的全纯函数族,n 1为任一正整数,b为有限常数,如果对F中任意两个函数f与g,fn(f-1)f′与gn(g-1)g′在D内都以b为公共值,则F在D内正规.此结果对亚纯函数不成立. 相似文献
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Let f be a generalized holomorphic function on a connected open set
. It is proved that f equals zero if and only if there exists a smooth curve and a set A of positive (one-dimensional) measure such that f takes zero value on A. Also, a holomorphic generalized function different from zero on the disc, which takes zero values on a dense G
δ-set of the disc, is constructed. The generalized zero set of a holomorphic function is introduced and studied in an analogous
way. 相似文献
17.
Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve
of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples
on the projective line.
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We study the Banach algebras of bounded holomorphic functions on the unit disk whose boundary values, having, in a sense,
the weakest possible discontinuities, belong to the algebra of semi-almost periodic functions on the unit circle. The latter
algebra contains as a special case an algebra introduced by Sarason in connection with some problems in the theory of Toeplitz
operators. 相似文献
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