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本文在三角Hopf代数表示范畴上系统地研究了Lie余代数,在此范畴上 的Lie余代数与Hopf代数之间建立了重要的联系.主要给出了Lie余代数的余包络 余代数的结构.所得结果自然是关于Lie代数的对偶结果,推广了 Sweedler M. E., Gurevich D.I., Michaelis W.和 Maiid S.等人的结果. 相似文献
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本文在三角Hopf代数表示范畴上系统地研究了Lie余代数,在此范畴上 的Lie余代数与Hopf代数之间建立了重要的联系.主要给出了Lie余代数的余包络 余代数的结构.所得结果自然是关于Lie代数的对偶结果,推广了 Sweedler M. E., Gurevich D.I., Michaelis W.和 Maiid S.等人的结果. 相似文献
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本文获得了几个压缩型映射的不动点定理,改进了相应文献的结果.应用该定理,给出了一类时滞积分方程的正概周期解的存在性结果.推广了已有的结果. 相似文献
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有限域 Fq(q为奇)上的 Kloosterman和是两个模为 q1/2的共轭复数之和.这个复数的角度就称为相应的Kloosterman和的角度.我们在本文给出了Kloosterman和的角度的一些结果,改进了Katz N.[1]的一些结果,也改进和推广了Conrey J.和Iwanie H.[2]的结果. 相似文献
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文[1]指出:此方程不是普通的方程,不能用常规的代数方法来解答.该题离开计算器已无法得到结果.笔者认为此题不用计算器可以得到结果. 相似文献
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将多元复分析中一种复偏微分方程组的解与复Clifford分析中双曲调和函数联系起来,并研究了双曲调和函数的几个性质。 相似文献
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讨论了Clifford分析中双曲调和函数的一个带位移的非线性边值问题,先讨论了解析函数的一个边值问题的解的存在性,然后利用Clifford分析中双曲调和函数与解析函数的关系讨论了此边值问题的解,并给出了解的积分表达式. 相似文献
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We prove the Mejia-Pommerenke conjecture that the Taylor coefficients of hyperbolically convex functions in the disk behave like O(log?2(n)/n) as n → ∞ assuming that the image of the unit disk under such functions is a domain of bounded boundary rotation. Moreover, we obtain some asymptotically sharp estimates for the integral means of the derivatives of such functions and consider an example of a hyperbolically convex function that maps the unit disk onto a domain of infinite boundary rotation. 相似文献
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Raymond Mortini 《Complex Analysis and Operator Theory》2011,5(1):219-235
We study the class of inner functions Q{\Theta} whose zero set Z(Q){Z(\Theta)} stays hyperbolically close to
[`(Z\mathbbD(Q))]{\overline{Z_\mathbb{D}(\Theta)}} on the corona of H
∞ and show that these functions are uniformly approximable by interpolating Blaschke products. 相似文献
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We initiate a study of harmonic functions on hypergroups. In particular, we introduce the concept of a nilpotent hypergroup and show such hypergroup admits an invariant measure as well as a Liouville theorem for bounded harmonic functions. Further, positive harmonic functions on nilpotent hypergroups are shown to be integrals of exponential functions. For arbitrary hypergroups, we derive a Harnack inequality for positive harmonic functions and prove a Liouville theorem for compact hypergroups. We discuss an application to harmonic spherical functions. 相似文献
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In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi-type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions. 相似文献
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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. 相似文献
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This paper investigates positive harmonic functions on domains that are complementary to a subset of a cylindrical surface.
It characterizes, both in terms of harmonic measure and of a Wiener-type criterion, those domains that admit minimal harmonic
functions with exponential growth. Illustrative examples are provided. Two applications are also given. The first of these
concerns minimal harmonic functions associated with an irregular boundary point, and amplifies a recent construction of Gardiner
and Hansen. The second concerns the possible non-approximability of positive harmonic functions by integrable positive harmonic
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This research was supported by Science Foundation Ireland under Grant 06/RFP/MAT057, and is also part of the programme of
the ESF Network “Harmonic and Complex Analysis and Applications” (HCAA). 相似文献
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Roger W. Barnard 《Journal of Mathematical Analysis and Applications》2011,384(2):366-374
We describe extremal functions for the generalized Fekete-Szegö functional over the class of hyperbolically convex functions. We apply the Julia variational formula to reduce the problem to mappings onto hyperbolic polygons having no more than two proper sides. In general, this is the best result possible. We show that both one-sided and two-sided maps can be extremal for different sub-classes. 相似文献
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The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated. The numerical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively. 相似文献