无界集合上的函数逼近

Function Approximation of Infinite Set

得到了函数系M(Λ)在C[e-p(z)]中完备的一个充分条件,其中C[e-p(z)]是所有在复平面的某个无界集合L上连续,且当z趋向无穷时,f(z)exp(-p(z))趋向零的复函数f组成的集合.在一致范数‖f‖=supz∈le-p(z)|f(z)|下,C[e-p(z)]是一个Banach空间.

Obtain a sufficient condition for the completeness of the system M（A） in C[e^-p（z）] ,where C[e^-p（z）] isa weighted Banach space of complex continuous functions f on some infinite set L on complex plane,with f（z）exp （-p（z） ） vanishing at infinity, in the uniform norm ｜｜f｜｜=supe-p（z）z∈l｜f（z）｜ with respect to the weight p（z）.