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Abstract <p> We consider the spectral problem for the operator <Equation ID="Equi"> <MediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3007_Article_Equi.gif" Format="GIF" Height="45" Rendition="HTML" Resolution="72" Type="Linedraw" Width="284" /> </MediaObject> <EquationSource Format="TEX">\(Af(x)=ixf(-x)+\int_{-1}^1K(x,y)f(y)\,dy\)</EquationSource> </Equation> acting in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3007_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2[-1,1]\)</EquationSource> </InlineEquation>. For a certain class of kernels <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3007_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> </InlineEquation>, we prove the finiteness of the discrete spectrum of the operator <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3007_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation>. In the case of a finite-dimensional perturbation, we also obtain sufficient conditions for the emptiness of the discrete spectrum. </p>

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Spectral Properties of the Friedrichs Model with Involution

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • G. A. Agafonkin

摘要

Abstract

We consider the spectral problem for the operator \(Af(x)=ixf(-x)+\int_{-1}^1K(x,y)f(y)\,dy\) acting in \(L_2[-1,1]\) . For a certain class of kernels \(K\) , we prove the finiteness of the discrete spectrum of the operator \(A\) . In the case of a finite-dimensional perturbation, we also obtain sufficient conditions for the emptiness of the discrete spectrum.