Hardy inequality and the construction of infinitesimal operators with non-basis family of eigenvectors

Grigory M. Sklyar; Vitalii Marchenko

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arXiv · 1405.2731

Hardy inequality and the construction of infinitesimal operators with non-basis family of eigenvectors

Grigory M. Sklyar·Vitalii Marchenko

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Abstract

Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete Hardy inequality plays an important role in the proposed approach. The construction complement the results of G.Q.~Xu et al.~\cite{Xu} (2005) and H.~Zwart~\cite{Zwart} (2010) on the Riesz basis property of eigenvectors (eigenspaces) of infinitesimal operators. Our results are extended to the case of operators on some Banach spaces.

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Grigory M. Sklyar, Vitalii Marchenko. 2014-05-12. Hardy inequality and the construction of infinitesimal operators with non-basis family of eigenvectors. https://arxiv.org/abs/1405.2731

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