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Abstract <p>We prove, that if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{\lambda_{n}\}_{n\in Z}\)</EquationSource> <!--ContMath2570025Harutyunyan-m1--> </InlineEquation> is the set of eigenvalues of selfadjoint Dirac operator on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((0,\pi)\)</EquationSource> <!--ContMath2570025Harutyunyan-m2--> </InlineEquation>, then the system <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\left\{\left(\begin{matrix}\sin\lambda_{n}x\\ -\cos\lambda_{n}x\end{matrix}\right)\right\}_{n\in Z}\)</EquationSource> <!--ContMath2570025Harutyunyan-m3--> </InlineEquation> is a Riesz bases in Hilbert space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^{2}([0,\pi]),C^{2})\)</EquationSource> <!--ContMath2570025Harutyunyan-m4--> </InlineEquation>.</p>

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Riesz Bases Generated by the Spectra of Dirac Operators

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • T. N. Harutyunyan

摘要

Abstract

We prove, that if \(\{\lambda_{n}\}_{n\in Z}\) is the set of eigenvalues of selfadjoint Dirac operator on \((0,\pi)\) , then the system \(\left\{\left(\begin{matrix}\sin\lambda_{n}x\\ -\cos\lambda_{n}x\end{matrix}\right)\right\}_{n\in Z}\) is a Riesz bases in Hilbert space \(L^{2}([0,\pi]),C^{2})\) .