Incompleteness of exponential system in the weighted Banach space. (English) Zbl 1149.30025
Summary: We take a new approach to obtain necessary and sufficient condition for the incompleteness of exponential system in \(C_\alpha\), where \(C_\alpha\) is the weighted Banach space of complex continuous functions \(f\) defined on the real axis \(\mathbb{R}\) source with \(f(t)\exp(-\alpha(t))\) vanishing at infinity, in the uniform norm.
MSC:
| 30E05 | Moment problems and interpolation problems in the complex plane |
| 41A30 | Approximation by other special function classes |
References:
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