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

Andrei V. Semenov

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

Hereditary completeness for systems of exponentials in weighted L²-spaces

Andrei V. Semenov This is my paper

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classification math.CV math.FA

keywords completeexponentialsweightedcompletenessdecayendpointsexistshereditarily

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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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Hereditary completeness for systems of exponentials in weighted L²-spaces

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