We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also consid...We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith＇s celebrated work （Journal of Functional Analysis 205 （2003） 62-89）. The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping.展开更多
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined ...We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.展开更多
基金Supported by the Natural Science Foundation of Yunnan Province (Grant No.2009ZC013X)Basic Research Foundation of Education Bureau of Yunnan Province (Grant No.09Y0079)
文摘We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith＇s celebrated work （Journal of Functional Analysis 205 （2003） 62-89）. The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping.
基金Supported by the Basic Research Foundation of Yunnan Province (Grant No. 2009ZC013X)the Basic Research Foundation of Education Bureau of Yunnan Province (Grant No. 09Y0079)
文摘We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.
