Hereditary completeness for systems of exponentials in weighted $L^2$-spaces

Andrei V. Semenov

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Hereditary completeness for systems of exponentials in weighted $L^2$-spaces

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arxiv 2503.18131 v3 pith:ZYX3BE6M submitted 2025-03-23 math.CV math.FA

Andrei V. Semenov This is my paper

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keywords completeexponentialsweightedcompletenessdecayendpointsexistshereditarily

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abstract

We prove that for any weight $w$, which has at most polynomial decay at the endpoints of the interval, there exists a complete and minimal system $\{e^{i\lambda_n t}\}_{n\in \mathbb{N}}$ of exponentials in the weighted space $L^2(w)$ which is not hereditarily complete.

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