| Exponential Polynomial Approximation with Unrestricted Upper Density |
| Received:February 05, 2009 Revised:October 14, 2009 |
| Key Words:
incompleteness Banach space exponential system.
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| Fund Project:Supported by the Basic Research Foundation of Yunnan Province (Grant No.2009ZC013X) and the Basic Research Foundation of Education Bureau of Yunnan Province (Grant No.09Y0079). |
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| Abstract: |
| We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in $L^{p}_{\alpha}$, where $L^{p}_{\alpha}$ is the weighted Banach space of complex continuous functions $f$ defined on the real axis $\mathbb{R}$ satisfying $(\int_{-\infty}^{ \infty}|f(t)|^{p}e^{-\alpha(t)}\d t)^{1/ p}$, $1 |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.020 |
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