上密度无限制的指数多项式逼近

Exponential Polynomial Approximation with Unrestricted Upper Density

中文关键词:  不完备性  Banach空间  指数多项式.

英文关键词:incompleteness  Banach space  exponential system.

中文摘要:

      我们采用新的方法讨论 $L^{p}_{\alpha}$ 空间中指数函数系的完备性, 其中 $L^{p}_{\alpha}$表示由实数轴$\mathbb{R}$ 上连续且满足$(\int_{-\infty}^{ \infty}|f(t)|^{p}e^{-\alpha(t)}\rm d{\it t})^{1/p}(1

英文摘要:

      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