共查询到19条相似文献,搜索用时 125 毫秒
1.
本文研究了推广的Poisson积分的增长性问题.利用复平面中经典的Hayman定理及其证明方法,通过修改上半空间中的Poisson积分,获得了上半空间中一类位势在无穷远点的增长性质,推广了Hayman定理在高维空间的结果. 相似文献
2.
修改的Poisson核和调和函数的积分表示 总被引:3,自引:0,他引:3
在本文中,对于半平面中的调和函数u(z),利用半平面中修改的Poisson核,证明了如果它的正部u~ (z)=max{u(z),0}满足某些限制增长条件,则它可以用半平面边界上的积分表示出来,并且它的负部u~-(z)=max{-u(z),0}也被类似的增长条件所控制,这一结果改进了在半平面中调和函数的某些经典结果。 相似文献
4.
利用Whitney方体的相关性质, 给出了一类调和函数在半空间中无穷远点处的增长估计, 且刻画了其
例外集的几何性质. 本文推广了张艳慧和邓冠铁在半空间中的相关结果. 相似文献
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1 引言及结果 设f是复平面C中超越亚纯函数.亚纯函数a_i(z)称为小函数,若a_i(z)满足T(r,a_i)=o(T(r,f))(i=1,2,…)。我们采用Nevanlinna理论中常用记号,用S(r,f)表示量:当f为有穷级时S(r,f)=O(log r);当f为无穷级时S(r,f)=O(log r T(r,f)),至多除去r的一个有限测度集。 相似文献
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基于向量旋转内积不变的特点,通过对Green积分公式的推广,得到与空间Green三个公式相似的平面Green公式.从而,得到平面中Poisson方程Robin问题的解和平面中Poisson方程Dirichlet问题的解. 相似文献
9.
本文证明了n-维(n≥2)Euclidean空间的上半空间中Poisson积分在无穷远点处的增长性质.同时将这个性质推广到次调和函数中去,其概括了解析函数和调和函数的增长性质. 相似文献
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Let (X
t
)
t⩾0 be the n-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space having the Laplace–Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer
transform of the Poisson kernel and the Green function of the ball for the process (X
t
)
t⩾0. Under additional hypotheses we prove integral representations for the Poisson kernel. This yields explicit formulas in and spaces for the Poisson kernel and the Green function as well.
相似文献
12.
In this paper, we construct a modified Green potential in the upper-half space of the n-dimensional Euclidean space. Meanwhile, the behavior at infinity of it is also given. 相似文献
13.
《Mathematical Methods in the Applied Sciences》2018,41(7):2811-2826
In this work, the modified Green function technique for the exterior Dirichlet problem in linear thermoelasticity is presented. Expressing the solution of the problem as a double‐layer potential of an unknown density, we form the associated boundary integral equation that describes the problem. Exploiting that the discrete spectrum of the irregular values of the associated integral equation is identified with the spectrum of eigenvalues of the corresponding interior homogeneous Neumann problem for the transverse part of the elastic displacement field, we introduce a modification of the fundamental solution of the elastic field. We establish the sufficient conditions that the coefficients of the modification must satisfy to overcome the problem of nonuniqueness for the thermoelastic problem. 相似文献
14.
In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C1,1-cylindrical domain . Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of . These results are first studied by some authors for certain elliptic and less general parabolic operators.
Mathematics Subject Classifications (2000) 31B25, 35B05, 35K10, 58J35. 相似文献
15.
Francisco Rodríguez 《Mathematische Nachrichten》1996,179(1):247-257
Some conditions on the size of the exceptional set that arise in Nevanlinna's Second Fundamental Theorem are established, showing that previous sharp results can be improved by restricting the class of functions considered and suggesting a close relationship between the size of the exceptional set and the lower growth of the characteristic function. Examples of functions of rapid growth possessing exceptional sets are built, showing that these conditions are sharp for the class of functions considered. 相似文献
16.
In this paper, we derive the non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions using a spectral cut-off function approach to impose a minimum length scale in the homogeneous solution. The resulting non-singular Green’s functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size ) and thus cannot handle the singular Green’s function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green’s function, as this is useful in applications where the Poisson equation represents potential functions of a vector field. 相似文献
17.
Piotr Kot 《Czechoslovak Mathematical Journal》2004,54(1):55-63
For z B
n, the boundary of the unit ball in
. If
the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if Eis a G
and F
subset of the projective (n– 1)-dimensional space
then there exists a holomorphic function fin the unit ball B
nso that E(f) = E. 相似文献
18.
《复变函数与椭圆型方程》2013,58(4):547-556
In this article, a modified Kelvin transform on ? n using inversion with respect to a ball of arbitrary radius is defined, which gives explicit expressions for Green's function and Poisson's kernel for the Korányi ball of arbitrary radius and annular domain. The solution of the Dirichlet problem for the union of two balls is discussed using the Schwarz's alternating method. 相似文献
19.
Steven G. Krantz 《Journal of Mathematical Analysis and Applications》2005,302(1):143-148
We provide a simple method for obtaining boundary asymptotics of the Poisson kernel on a domain in RN. 相似文献