共查询到17条相似文献,搜索用时 93 毫秒
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谢永红 《数学年刊A辑(中文版)》2014,35(2):235-246
研究了取值于实Clifford代数空间Cl_(n+1,0)(R)中对偶的k-hypergenic函数.首先,给出了对偶的k-hypergenic函数的一些等价条件,其中包括广义的Cauchy-Riemann方程.其次,给出了对偶的hypergenic函数的Cauchy积分公式,并且应用其证明了(1-n)-hypergenic函数的Cauchy积分公式.最后,证明了对偶的hypergenic函数的Cauchy积分公式右端的积分是U\Ω_2中对偶的hypergenic函数. 相似文献
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泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式 总被引:1,自引:0,他引:1
本文研究了泛Clifford分析中的Cauchy积分公式和Cauchy-Pompeiu公式.通过引入修正的Cauchy核,得出了取值在泛Clifford代数上的两公式在无界域上的表达式.此两公式是有界域上的相应结果的推广,并为研究无界域上的边值问题打下了基础. 相似文献
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主要研究了两类函数的Cauchy积分公式及其相关问题.首先给出了Clifford分析中右hypergenic函数的Cauchy积分公式,其次研究了右hypergenic函数拟Cauchy型积分的性质,最后给出了Clifford分析中双hypergenic函数的Cauchy积分公式. 相似文献
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蔡好涛 《数学物理学报(A辑)》2006,26(3):421-425
该文首先给出Cauchy型主值积分φ(wf,x)的一种求积公式φm*(wf,x),然后证明序列$φm*(wf,x)}m=2∞在整个闭区间[-1,1]上是一致收敛到Cauchy型主值积分φ(wf,x)的,同时给出它的误差界. 相似文献
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对比于多复变中的Bochner-Martinelli型积分的Plernelj公式,定义了艾米尔特Clifford分析中旋量值函数的Cauchy型积分及Cauchy主值积分,得到了旋量值函数的Plemelj公式,最后给出一些特殊情形的Bochner-Martinelli型积分的Plemelj公式. 相似文献
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以拟Cauchy型积分公式及超正则函数的Plemelj公式为基础,进一步研究了拟Cauchy型积分的Holder连续性:即对两点都在边界上;一点在边界上,另一点在区域内(区域外);两点都在区域内(两点都在区域外)这三种情形分别进行了研究. 相似文献
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在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计. 相似文献
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In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries. 相似文献
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该文由泛Clifford分析中在特异边界上的Cauchy积分式得出了具有孤立奇点的LR正则函数在其相应的Laurent域上的Laurent展式,并由此给出了留数的定义,得出了类似于经典函数理论的留数定理。 相似文献
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Vladislav V. Kravchenko 《Journal of Mathematical Analysis and Applications》2008,339(2):1103-1111
We present a new technique for explicit construction of Cauchy kernels and Cauchy integral representations for a class of generalized analytic functions and p-analytic functions. 相似文献
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Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called Dirac operator, which factorizes the Laplacian; monogenic functions may thus also be seen as a generalization of holomorphic functions in the complex plane. Hermitian Clifford analysis offers yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitian (or h-) monogenic functions, of two Hermitian Dirac operators which are invariant under the action of the unitary group. In Brackx et al. (2009) [8] a Clifford-Cauchy integral representation formula for h-monogenic functions has been established in the case of domains with smooth boundary, however the approach followed cannot be extended to the case where the boundary of the considered domain is fractal. At present, we investigate an alternative approach which will enable us to define in this case a Hermitian Cauchy integral over a fractal closed surface, leading to several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations. 相似文献
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Damián Pinasco 《Journal of Mathematical Analysis and Applications》2005,308(1):159-174
In this paper we discuss the problem of integral representation of analytic functions over a complex Banach space E. We obtain, for a wide class of functions, integral representations of the form
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Ding-dong Gong 《高校应用数学学报(英文版)》2008,23(3):273-278
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well. 相似文献