复指数多项式在半带形中的完备性

对复指数多项式在Banach空间Hα中的完备性给出了充分必要条件,其中Hα为在半带形Iα={z=x+iy:x≥0,|y|≤α}(α>0)中连续,在Iα的内部解析且当x→∞时,f(x+iy)在Iα中关于y一致地趋向0的函数f(x+iy)全体,其范数为上确界范数.

复指数多项式在Hardy空间中的完备性

对复指数多项式在Banach空间Hpα(1≤p≤2)中的完备性给出了充要条件,其中Hpα为开半带形Iα={z=x+iy:x>0,|y|<α}(α>0)中的Hardy空间.

复指数多项式在半带形中的完备性

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.

On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin＇s classical results.