Approximation of Müntz-Szász type in weighted spaces

The paper looks at whether a system of exponentials $\exp(-\lambda_nt)$, $\operatorname{Re}\lambda_n>0$, is complete in various function spaces on the half-line $\mathbb R_+$. Wide classes of Banach spaces $E$ and $F$ of functions on $\mathbb R_+$ are described such that this system is complete in $E$ and $F$ simultaneously. A test is established to determine when this system is complete in the weighted spaces $C_0$ and $L^p$ with weight $(1+t)^\alpha$ on $\mathbb R_+$, for $\alpha<0$ and $\alpha<-1$, respectively.
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