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1.
The notion of Kuratowski convergence is applied to describe a kind of convergence in the context of holomorphic functions. We associate it to a convenient topology, explore its relation with the compact-open topology, thus providing a new set theoretic point of view of this classic topology, and present it in the framework of set-valued mappings.  相似文献   

2.

In this paper, suppose that ? m (z)(m = 1,2,…) are of infinite order. Applying the notion of infinite type [4], we obtain the sufficient conditions for uniform convergence of sequence of holomorphic functions in the unite disk.  相似文献   

3.
The purpose of this paper is to present extended results on convergence of a method for coupling of an analytical and a finite element solution for a boundary value problem with a singularity. As an example of a singular problem we consider a solution to the Lamé-Navier equation with a singularity caused by a crack. The main idea of such an approach is to construct a continuous coupling between an analytical solution near a singularity and a finite element solution through the whole interaction interface. In this paper we present a basic theory of convergence for a method of coupling, particularly we discuss some points which show a difference to the standard theory of the finite element method.  相似文献   

4.
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   

5.
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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7.
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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9.
吕锋  徐俊峰  仪洪勋 《数学学报》2010,53(5):963-974
本文证明了两个正规族定理,分别改进了张国明、孙伟和庞学诚的一个结果和徐焱的一个结果.  相似文献   

10.
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   

11.
Let f be a generalized holomorphic function on a connected open set W ì \Bbb C\Omega\subset {\Bbb C} . 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   

12.
Let D be a C-convex domain in C n . Let , and d = 0,1,2, ..., be an array of points in a compact set . Let f be holomorphic on and let K d (f) denote the Kergin interpolating polynomial to f at A d0 ,... , A dd . We give conditions on the array and D such that . The conditions are, in an appropriate sense, optimal. This result generalizes classical one variable results on the convergence of Lagrange—Hermite interpolants of analytic functions. Date received: October 21, 1995. Date revised: May 1, 1996.  相似文献   

13.
Let φ be a plurisubharmonic function on a pseudoconvex domain D in an n-dimensional complex space. We show that there exists a nonzero holomorphic function f on D such that some local mean value of φ with logarithmic additional terms majorizes log|f|. A similar problem is discussed for a locally integrable function on D in terms of balayage of positive measures.  相似文献   

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15.
Let V be n-dimensional complex vector space. The aim of this paper is to give an elementary proof of the isomorphism O t V ^[n] O t V*, which quantizes the Fourier–Sato transform of the conic sheaf O t V of temperate holomorphic functions  相似文献   

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For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology on the space of holomorphic functions from U into F. This topology allows us to construct a predual for which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions.  相似文献   

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19.
It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on Ω, which is equal to zero in an open set L ì WL\subset{\rm{\Omega}} , is equal to zero.  相似文献   

20.
Cowen and Pommerenke obtained inequalities for fixed pointsof holomorphic and univalent functions in [1]. There was onlyone case where their inequality was not the best possible. Byan entirely new method, we will establish a sharp improvementto this case and provide simple proofs to their main resultsin [1]  相似文献   

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