On the Riesz Means of Expansions by Riesz Bases Formed by Eigenfunctions of the Schrödinger Operator

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1987 English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 18, pages 59-71 (issn: 0031-5303, eissn: 1588-2829,

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Authors: Loi, N. H.;

doi: 10.1007/bf01849034

On the Riesz Means of Expansions by Riesz Bases Formed by Eigenfunctions of the Schrödinger Operator

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Abstract

The author proves a result on the convergence of Riesz means of expansions with respect to Riesz bases \(\{u_ k\}\) of \(\sigma_ k\)-th order eigenfunctions of a nonself-adjoint one-dimensional Schrödinger operator on a bounded interval. The result extends earlier results of \textit{I. Joó} and \textit{V. Komornik} [Acta. Sci. Math. 46, 357-375 (1983; Zbl 0537.34019)] to the case where Im \(\sqrt{\lambda_ k}\) needs not be bounded.

Related Organizations

Eötvös Loránd University
Hungary

Keywords

Schrödinger operator, Ordinary differential operators, Special methods of summability, Riesz means, Riesz bases

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