Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball

For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.

     

A Schwarz Lemma for Harmonic Mappings Between the Unit Balls in Real Euclidean Spaces

The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.     

Double integral characterizations of harmonic Bergman spaces

Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space.     

Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.     

A maximum principle for harmonic mappings which solve a Dirichlet problem

We show that if a solution of the Dirichlet problem for harmonic maps lies in a convex ball and its boundary values are contained in some smaller ball, then the whole solution itself is contained in this smaller ball.     

求解Fisher型方程的混合Jacobi-球面调和谱方法

本文提出了两种数值求解单位球内Fisher型方程的混合Jacobi-球面调和谱格式,并分别给出了格式的收敛性及相关的数值结果。     

Harmonic functions on the real hyperbolic ball II Hardy‐Sobolev and Lipschitz spaces

In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started in [13]. Our focus here is on the theory of Hardy‐Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman‐Stein like characterizations in terms of maximal and square functionals. We further prove that the hyperbolic harmonic extension of Lipschitz functions on the boundary extend into Lipschitz functions on the whole ball. In doing so, we exhibit differences of behaviour of derivatives of harmonic functions depending on the parity of the dimension of the ball and on the parity of the order of derivation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jost maps, ball-homogeneous and harmonic manifolds

Given a real number ε>0, small enough, an associated Jost map J_ε between two Riemannian manifolds is defined. Then we prove that connected Riemannian manifolds for which the center of mass of each small geodesic ball is the center of the ball (i.e. for which the identity is a J_ε map) are ball-homogeneous. In the analytic case we characterize such manifolds in terms of the Euclidean Laplacian and we show that they have constant scalar curvature. Under some restriction on the Ricci curvature we prove that Riemannian analytic manifolds for which the center of mass of each small geodesic ball is the center of the ball are locally and weakly harmonic.     

Stability and vibration analysis of a complex flexible rotor bearing system

This paper presents the non-linear dynamic analysis of a flexible rotor having unbalanced and supported by ball bearings. The rolling element bearings are modeled as two degree of freedom elements where the kinematics of the rolling elements are taken into account, as well as the internal clearance and the Hertz contact non-linearity. In order to calculate the periodic response of this non-linear system, the harmonic balance method is used. This method is implemented with an exact condensation strategy to reduce the computational time. Moreover, the stability of the non-linear system is analyzed in the frequency-domain by a method based on a perturbation applied to the known harmonic solution in the time domain.     

Bounded harmonic maps on a class of manifolds

Without imposing any curvature assumptions, we show that bounded harmonic maps with image contained in a regular geodesic ball share similar behaviour at infinity with the bounded harmonic functions on the domain manifold.

     

调和函数的Lipschitz型空间和Landau-Bloch型定理

主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.     

用混合Jacobi-球面调和拟谱方法数值求解Fisher型方程

本文提出了一种数值求解单位球内Fisher型方程的全离散混合Jacobi-球面调和拟谱格式,数值结果显示该方法是有效的.     

ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS FROM COMPLETE MANIFOLDS

51.IntroductionLetMbeanm-dimensionalcompletenoncompactRiemannianmanifold,pEM.P.LiandL.F.Turnintroducedin[8]avolumecomparisoncondition(VC)(seethedefinitionbelow).TheyobtainedsomeimportantanalyticpropertiesifMsatisfies(VC)andtheRiccicurvatureconditionRice(x)2--(m--1)K/(1 r(x))',wherer(x)isthedistancefromptox,K20isaconstant.ItisinterestingtoknowmoreabouttheanalysisonsuchamanifoldM.LetNbeacompleteRiemannianmanifoldwiththesectionalcurvatureKNboundedabovebysomeconstantK20.B.(T)denotestheg…     

Extreme harmonic functions on a ball

In order to show that one can recapture the Riesz-Herglotz theorem from the Krein-Milman theorem, we determine directly the set of extreme points of the convex set of positive harmonic functions on the unit ball (normalized by 1 at the origin). The characterization is obtained using standard facts from abstract analysis combined with a minimum of very basic results on harmonic functions.     

On the largest ball of harmonic continuation

An expression is derived for the radius of the largest ball, centred at a given point, into which a function, harmonic in a neighbourhood of that point, can be harmonically continued.     

复调和函数及其在无穷远点的性质

本文讨论了复调和函数在无穷远点的性质,揭示出有界区域上复调和函数的两类表示式之间的关系.     

Concentrated boundary data and axially symmetric harmonic maps

We examine the existence problem for harmonic maps between the three-dimensional ball and the two-sphere. We utilize results on the classification of harmonic maps into hemispheres and a result on the regularity of the weak limit of energy minimizers over the class of axially symmetric maps to establish the existence of asmooth harmonic extension for boundary data suitably “concentrated” away from the axis of symmetry. In addition, we establish convergence results for the harmonic map heat flow problem for suitably “concentrated” axially symmetric initial and boundary data.     

The gradient of certain harmonic functions on manifolds of almost nonnegative Ricci curvature

In this paper we prove that when the Ricci curvature of a Riemannian manifoldM ⁿ is almost nonnegative, and a ballB _L (p)⊂M ⁿ is close in Gromov-Hausdorff distance to a Euclidean ball, then the gradient of the harmonic functionb defined in [ChCo1] does not vanish. In particular, these functions can serve as harmonic coordinates on balls sufficiently close to an Euclidean ball. The proof, is based on a monotonicity theorem that generalizes monotonicity of the frequency for harmonic functions onR ⁿ .     

半离散Jacobi-球面调和谱格式用于流体低马赫数流动

本文提出了一种用于解决流体在球内以低马赫数流动问题的半离散Jacobi-球面调和谱格式,并证明了它的稳定性和收敛性.所用技巧也可应用于球形区域上其它非线性问题.     

Ultradistributional boundary values of harmonic functions on the sphere

We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calderón and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.