共查询到20条相似文献,搜索用时 31 毫秒
1.
LetDR2be the open unit disk. We consider best harmonic approximation to functions continuous onD. In a basic paper, Haymanet al.characterized best harmonic approximants which are themselves continuous onD. In this paper we give sufficient conditions and many simple examples of functions continuous onDwhich have no best harmonic approximants which are continuous onD. 相似文献
2.
Z. R. Pop-Stojanović 《Journal of Theoretical Probability》1989,2(4):503-508
In an earlier paper(4) the author has shown that a diffusion process whose potential kernel satisfies certain analytic conditions has all of its excessive harmonic functions, which are not identically infinite, continuous. This paper shows that under these conditions (concerning its potential kernel), the excessiveness of its nonnegative harmonic functions isautomatic. 相似文献
3.
A. A. Malyarenko 《Ukrainian Mathematical Journal》1999,51(1):66-75
We consider local properties of smaple functions of Gaussian isotropic random fields on compact Riemannian symmetric spacesM of rank 1. We give conditions under which the sample functions of a field almost surely possess logarithmic and power modulus
of continuity. As a corollary, we prove a theorem of the Bernstein type for optimal approximations of functions of this sort
by harmonic polynomials in the metric of the spaceL
2(M). We use theorems of the Jackson-Bernstein-type to obtain sufficient conditions for the sample functions of a field to almost
surely belong to the classes of functions associated with the Riesz and Cesàro means.
International Mathematical Center, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal,
Vol. 51, No. 1, pp. 60–68, January, 1999. 相似文献
4.
《Applied Mathematics Letters》2003,16(6):905-909
Ruscheweyh and Sheil-Small proved the PólyarSchoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that close-to-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve close-to-convexity under convolution. An auxiliary function enables us to obtain necessary and sufficient convolution conditions for convex and starlike harmonic functions, which lead to sufficient coefficient bounds for inclusion in these classes. 相似文献
5.
R. R. Kocherlakota 《Aequationes Mathematicae》1986,31(1):109-117
We consider the collection of functions of one quaternion variable which can be expressed asG(Y) whereY is a real-valued quaternion function andG is a differential operator which corresponds to the gradient of real variable theory. Integral theorems for such functions are given, together with necessary and sufficient conditions for a function to be a gradient function, in terms of its Frechet derivative. The extended complex analytic functions, the Fueter functions, and the momentum-energy density functions are seen to be gradient functions which correspond to biharmonic, harmonic, and wave functions respectively. 相似文献
6.
For a non-compact harmonic manifold M, we establish an integral formula for the derivative of a harmonic function on M. As
an application we show that for the harmonic spaces having minimal horospheres, bounded harmonic functions are constant. The
main result of this article states that the harmonic spaces having polynomial volume growth are flat. In other words, if the
volume density function Θ of M has polynomial growth, then M is flat. This partially answers a question of Szabo namely, which
density functions determine the metric of a harmonic manifold. Finally, we give some natural conditions which ensure polynomial
growth of the volume function. 相似文献
7.
In our study of electrical networks we develop two themes: finding explicit formulas for special classes of functions defined on the vertices of a transient network, namely monopoles, dipoles, and harmonic functions. Secondly, our interest is focused on the properties of electrical networks supported on Bratteli diagrams. We show that the structure of Bratteli diagrams allows one to describe algorithmically harmonic functions as well as monopoles and dipoles. We also discuss some special classes of Bratteli diagrams (stationary, Pascal, trees), and we give conditions under which the harmonic functions defined on these diagrams have finite energy.
相似文献8.
9.
In this paper, we mainly study the Rm (m>0) Riemann boundary value problems for functions with values in a Clifford algebra C?(V3, 3). We prove a generalized Liouville‐type theorem for harmonic functions and biharmonic functions by combining the growth behaviour estimates with the series expansions for k‐monogenic functions. We obtain the result under only one growth condition at infinity by using the integral representation formulas for harmonic functions and biharmonic functions. By using the Plemelj formula and the integral representation formulas, a more generalized Liouville theorem for harmonic functions and biharmonic functions are presented. Combining the Plemelj formula and the integral representation formulas with the above generalized Liouville theorem, we prove that the Rm (m>0) Riemann boundary value problems for monogenic functions, harmonic functions and biharmonic functions are solvable. Explicit representation formulas of the solutions are given. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
Yin Weiping 《数学学报(英文版)》1989,5(1):57-63
In this paper we get the invariant functions and the invariant harmonic functions under Aut (D) for certain Reinhardt domainsD. By using the invariant functions, we get much more invariant Kahler metrics. And the Ricci curvatures, scalar curvatures and holomorpic sectional curvatures are also obtained, which are very different for the bounded homogeneous domains. 相似文献
11.
Sirkka-Liisa Eriksson Marko Kotilainen Visa Latvala 《Advances in Applied Clifford Algebras》2007,17(3):425-436
Harmonic functions with respect to the Poincare metric on the unit ball are called hyperbolic harmonic functions. We establish
the weak formulation of hyperbolic harmonic functions and use it in the study of hyperbolic harmonic function spaces. In particular,
we give the Carleson measure characterization for the whole spectrum of spaces, whose analytic counterparts include among
else Bloch spaces, Bergman-spaces, Besov-spaces, and Qp-spaces.
The second author was supported by the Finnish Cultural Foundation. 相似文献
12.
《复变函数与椭圆型方程》2012,57(3):155-167
This article gives two types of conditions for a set E in a cylinder such that all positive harmonic functions in the cylinder which (essentially) majorize a minimal function at +∞ on E majorize it on the whole cylinder. 相似文献
13.
Clare D'Cruz 《代数通讯》2013,41(2):693-698
In an upcoming article we study harmonic analysis on the quantum E(2) group within an algebraic framework: we explicitly construct Fourier transforms between quantum E(2) and its Pontryagin dual, involving q-Bessel functions as kernel, prove Plancherel &; inversion formulas etc. In the present paper we propose an algebraic setting in which to perform harmonic analysis on non-compact, non-discrete quantum groups and in particular on quantum E(2). We are mainly concerned with the construction of positive and faithful invariant functionals on an algebraic level, KMS properties, etc. 相似文献
14.
In this paper we introduce a large class of subordinators called special subordinators and study their potential theory. Then
we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open set
D with special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed
symmetric stable process and the nonnegative harmonic functions of the subordinate killed symmetric stable process. We show
that nonnegative harmonic functions of the subordinate killed symmetric stable process are continuous and satisfy a Harnack
inequality. We then show that, when D is a bounded κ-fat set, both the Martin boundary and the minimal Martin boundary of the subordinate killed symmetric stable
process in D coincide with the Euclidean boundary ∂D.
The research of this author is supported in part by MZOS grant 0037107 of the Republic of Croatia and in part by a joint US-Croatia
grant INT 0302167. 相似文献
15.
This paper studies algebras of functions on the unit disk generated byH
∞(D) and bounded harmonic functions. Using these algebras, we characterize compact semicommutators and commutators of Toeplitz
operators with harmonic symbols on the Bergman space.
Supported in part by the National Science Foundation and the University Research Council of Vanderbilt University. 相似文献
16.
Yan Hui Zhang 《Mathematical Methods in the Applied Sciences》2019,42(12):4360-4364
In this article, we firstly discuss a kind of Phragemén‐Lindelöf Principle of harmonic functions by using the Nevanlinna's representation in the high dimensional space. Secondly, we derive the sufficient conditions for subharmonic functions being in the Nevanlinna class as well. These results are main tools to study the Hilbert space of harmonic functions with analytic approaches and generalizations of some classic results. 相似文献
17.
Collet Pierre Martínez Servet Martín Jaime San 《Probability Theory and Related Fields》2003,125(3):350-364
Using a new inequality relating the heat kernel and the probability of survival, we prove asymptotic ratio limit theorems
for the heat kernel (and survival probability) in general Benedicks domains. In particular, the dimension of the cone of positive
harmonic measures with Dirichlet boundary conditions can be derived from the rate of convergence to zero of the heat kernel
(or the survival probability).
Received: 31 March 2002 / Revised version: 12 August 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 60J65, 31B05
Key words or phrases: Positive harmonic functions – Ratio limit theorems – Survival probability 相似文献
18.
《Quaestiones Mathematicae》2013,36(4):527-530
In this paper, we prove that there exists an infinite dimensional closed vector space M of harmonic functions in R n such that each v ? M \{0} is a universal harmonic function. 相似文献
19.
Yuguang Shi You-De Wang 《Calculus of Variations and Partial Differential Equations》2000,10(2):171-196
In this paper we consider the Dirichlet problem at infinity of proper harmonic maps from noncompact complex hyperbolic space
to a rank one symmetric space N of noncompact type with singular boundary data . Under some conditions on f, we show that the Dirichlet problem at infinity admits a harmonic map which assumes the boundary data f continuously.
Received: March 11, 1999 / Accepted April 23, 1999 相似文献
20.
Liao Ming 《数学学报(英文版)》1989,5(1):9-15
Given a Markov process satisfying certain general type conditions, whose paths are not assumed to be continuous. LetD be an open subset of the state spaceE. Any bounded function defined on the complement ofD extends to be a function onE such that it is harmonic inD and satisfies the Dirichlet boundary condition at any regular boundary point ofD. The relation between harmonic functions and the characteristic operator of the given process is discussed. 相似文献