| 半平面中解析函数的积分表示及在逼近中的应用 |
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| 引用本文： | 杨向东,邓冠铁.半平面中解析函数的积分表示及在逼近中的应用[J].数学物理学报(A辑),2008,28(6):1242-1250. |
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| 作者姓名： | 杨向东 邓冠铁 |
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| 作者单位： | [1]昆明理工大学数学系,昆明650093 [2]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875 |
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| 基金项目： | 昆明理工大学人才引进项目(14118029)资助 |
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| 摘 要： | 在该文中, 作者证明了满足一定增长性条件的右半平面上的解析函数可以由它在边界上的积分和其加权Blaschke乘积的和表示, 作为应用, 作者还考虑了指数多项式在实数轴上加权 Banach 空间Cα 中的完备性.
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| 关 键 词： | 解析函数 Blaschke 乘积 积分表示 完备性 |
| 收稿时间： | 2006-12-01 |
| 修稿时间： | 2008-03-01 |
Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation |
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| Yang Xiangdong,Deng Guantie.Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation[J].Acta Mathematica Scientia,2008,28(6):1242-1250. |
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| Authors: | Yang Xiangdong Deng Guantie |
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| Institution: | (1.Department of Mathematics, Kunming University of Techonology, Kunming 650093；2.School of Mathematics Sciences, Key Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875） |
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| Abstract: | In this paper, we prove that analytic functions in the right half plane with some restricted growth can be represented by a sum of its weighted Blaschke product and its integral on the boundary of the half plane. As its applications, we also investigate the completeness of complex exponential polynomials inCα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f(t)exp(-α(t)) vanishing at infinity, in the uniform norm with respect to the weight α(t). |
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| Keywords: | Analytic functionszz Blaschke productzz Integral representationzz Completenesszz |
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