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<p>In this paper, we examine the convergence of eigenfunction expansions of a functional-differential operator with involution <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nu (x)=1-x\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ν</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation>, which is defined on a geometric graph consisting of two edges, one of which is a loop. Sufficient conditions are obtained for the uniform convergence of the Fourier series in the eigenfunctions of the operator (an analog of the Jordan–Dirichlet theorem).</p>

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AN ANALOG OF THE JORDAN–DIRICHLET THEOREM FOR AN OPERATOR WITH INVOLUTION ON A GRAPH

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • E. I. Biryukova

摘要

In this paper, we examine the convergence of eigenfunction expansions of a functional-differential operator with involution \(\nu (x)=1-x\) ν ( x ) = 1 - x , which is defined on a geometric graph consisting of two edges, one of which is a loop. Sufficient conditions are obtained for the uniform convergence of the Fourier series in the eigenfunctions of the operator (an analog of the Jordan–Dirichlet theorem).