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1.
Let D ? ? n be a domain with smooth boundary ?D, let E??D be a subset of positive Lebesgue measure mes(E) > 0, and let F ? G be a nonpluripolar compact set in a strongly pseudoconvex domain D ? ? m . We prove that, under an additional condition, each function separately analytic on the set X = (D × F) ∪ (E × G) has a holomorphic contination to the domain $\rlap{--} X = \{ (z,w) \in D \times G:\omega _{in}^ * (z,E,D) + \omega ^ * (w,F,D) < 1\} $ , where ω* is the P-measure and ω*in is the interior P-measure.  相似文献   

2.
The main result of the paper is as follows.Theorem. Suppose that G(z) is an entire function satisfying the following conditions: 1) the Taylor coefficients of the function G(z) are nonnegative: 2) for some fixed C>0 and A>0 and for |z|>R0, the following inequality holds:
Further, suppose that for some fixed α>0 the deviation DN of the sequence xn={αn}, n=1, 2, ..., as N→∞ has the estimate DN=0(lnB N/N). Then if the function G(z) is not an identical constant and the inequality B+1<A holds, then the power series converging in the disk |z|<1 cannot be analytically continued to the region |z|>1 across any arc of the circle |z|=1. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 540–550, October, 1999.  相似文献   

3.
Let u(x) be a function analytic in some neighborhood D about the origin, $ \mathcal{D} Let u(x) be a function analytic in some neighborhood D about the origin, ⊂ ℝ n . We study the representation of this function in the form of a series u(x) = u 0(x) + |x|2 u 1(x) + |x|4 u 2(x) + …, where u k (x) are functions harmonic in . This representation is a generalization of the well-known Almansi formula. Original Russian Text ? V. V. Karachik, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 2, pp. 142–162.  相似文献   

4.
殷慰萍 《数学进展》1997,26(4):323-334
本文对一类拟凸域E(m,n,K)给出其不变Kahler度量下的全纯截曲率的显表达式,并构造了E(m,n,K)的一个不变的完备的Kahler度量,使得它大于或等于Bergman度量,而且其全纯截曲率的上界是一个负常数,从而得到E(m,n,K)的Bergman度量和Kobayashi度量的比较定理。  相似文献   

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6.
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane.  相似文献   

7.
We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ?   and we denote by u?u? the corresponding solution. The behavior of u?u? for ?   small and positive can be described in terms of real analytic functions of two variables evaluated at (?,1/log??)(?,1/log??). We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by u?u? for ?   small and describe u?u? by real analytic functions of ?. Then it is natural to ask what happens when ? is negative. The case of boundary data depending on ? is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem.  相似文献   

8.
We study the boundary values of the functions of the Sobolev function spaces W l and the Nikol’ski? function spaces H l which are defined on an arbitrary domain of a Carnot group. We obtain some reversible characteristics of the traces of the spaces under consideration on the boundary of the domain of definition and sufficient conditions for extension of the functions of these spaces outside the domain of definition. In some cases these sufficient conditions are necessary.  相似文献   

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We prove that Fredholm composition operators acting on the uniform algebra H(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.  相似文献   

12.
The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in one angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.H. Zheng [J.H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Elliptic Equ. 48 (9) (2003) 777-785] is completely answered. Furthermore, we give an example to explain the necessity of the condition
  相似文献   

13.
The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are considered. Theorems about normal families are formulated and proved in the language of these various topologies. Normal functions are also introduced. Characterizations in terms of automorphisms and also in terms of invariant derivatives are presented.  相似文献   

14.
In this note, the existence of translation-universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets. Corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of harmonic functions on the plane. Moreover, it is shown the existence of entire functions which are bounded on many rays and, simultaneously, are universal with respect to a prescribed infinite-order differential operator.  相似文献   

15.
In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.  相似文献   

16.
Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K =mn+1/m+n,m>1, the explicit forms of the complete Einstein-Kahler metrics are obtained.  相似文献   

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18.
We study the class of functions called monodiffric of the second kind by Isaac.They are discrete analogues of holomorphic functions of one or two complex variables.Discrete analogues of the Cauchy-Riemann operator,of domains of holomorphy in one discrete variable,and of the Hartogs phenomenon in two discrete variables are investigated.Two fundamental solutions to the discrete Cauchy-Riemann equation are studied:one with support in a quadrant,the other with decay at infinity.The first is easy to construct by induction;the second is accessed via its Fourier transform.  相似文献   

19.
We prove the converse of the trace theorem for the functions of the Sobolev spaces W p l on a Carnot group on the regular closed subsets called Ahlfors d-sets (the direct trace theorem was obtained in one of our previous publications). The theorem generalizes Johnsson and Wallin’s results for Sobolev functions on the Euclidean space. As a consequence we give a theorem on the boundary values of Sobolev functions on a domain with smooth boundary in a two-step Carnot group. We consider an example of application of the theorems to solvability of the boundary value problem for one partial differential equation.  相似文献   

20.
关于某类Reinhardt域的Bergman核函数与解析自同构最大群   总被引:1,自引:0,他引:1  
童武 《数学研究》1995,28(2):69-75
本文给出了Reinhardt域D={z=(z1,z2,z3)∈:|z1|2k+|z2|+|z3|2<1,k>0}的Bergman核函数,Bergman度量方阵及其解析自同构最大群。  相似文献   

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