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COMPLETENESS OF COMPLEX EXPONENTIAL POLYNOMIALS IN A HALF STRIP

CHEN Guodong DENG Guantie(School of Mathematical Sciences,Key Leboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,100875,Beijing,China)  
A necessary and sufficient condition was obtained for completeness of complex exponential polynomials in Banach spaces Mpα(1≤p∞),which was defined by functions f(z) satisfied analysis in Iα and sups0,0tα{∫Is,t|f(z)|p|dz|}∞ with Is,t={z:z=x+iy,xs,|y|t},Iα=I0,α.If in-completeness held,each function in the enclosure of the linear span of complex exponential system could be extended to an analytic function represented by series.
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