半平面中解析函数的积分表示及在逼近中的应用

Acta mathematica scientia,Series A

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Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation

Yang Xiangdong¹;Deng Guantie²

(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）

Received:2006-12-01 Revised:2008-03-01 Online:2008-12-25 Published:2008-12-25
Contact: Deng Guantie

Abstract

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 in
C_α, where C_α 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).

Key words: Analytic functions, Blaschke product, Integral representation, Completeness

CLC Number:

30E20

Yang Xiangdong;Deng Guantie. Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation[J].Acta mathematica scientia,Series A, 2008, 28(6): 1242-1250.

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Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation

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