摘要
给出了复指数多项式系在Banach空间Mαp(1≤p<∞)中完备的充要条件,其中Mαp是由在Iα中解析,且sups>0,0<t<α{∫Is,t|f(z)|p|dz|}<∞的函数组成,这里Is,t={z:z=x+iy,x>s,|y|<t},Iα=I0,α.并且证明了当复指数多项式系在Mαp中不完备时,其闭包中的函数可以扩张成用级数的形式表示的解析函数.
A necessary and sufficient condition was obtained for completeness of complex exponential polynomials in Banach spaces M^pα（1≤p〈∞）, which was defined by functions f（z） satisfied analysis in Io and sup s〉0,0〈t〈α{∫Is,t│f（z）│^p│dz│}〈∞. with Is,t{z：z=x＋iy,x〉s,│y│〈f},Iα=Io,α If in-completeness held, dais,t each function in the enclosure of the linear span of complex exponential system could be extended to an analytic function represented by series.
出处
《北京师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第4期362-367,共6页
Journal of Beijing Normal University(Natural Science)
基金
国家自然科学基金资助项目(10671022)
教育部博士点基金资助项目(20060027023)
关键词
复指数多项式
完备性
解析函数
complex exponential polynomials
completeness
analytic function
