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Stability of completeness for systems of exponentials on compact convex sets in \(\mathbb C\). (English. Russian original) Zbl 1037.30004

Math. Notes 72, No. 4, 542-550 (2002); translation from Mat. Zametki 72, No. 4, 587-596 (2002).
Summary: A sufficient condition for the stability of completeness of systems of exponentials \(\{\exp\lambda_nz\}\) with exponent shifts \(\lambda_n\) in spaces of functions continuous on and holomorphic inside a compact convex set \(K\subset \mathbb{C}\) with nonempty interior is obtained. This condition is a generalization of an important special case of the corresponding result for the closed interval due to Redheffer and Alexander.

MSC:

30B60 Completeness problems, closure of a system of functions of one complex variable
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