Scholarlink

Abstract <p> In this paper, we consider the Bloch eigenvalues and spectrum of the non-self-adjoint differential operator <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1171_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(L\)</EquationSource> </InlineEquation> generated by the differential expression of odd order <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1171_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation> with periodic <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1171_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{PT}\)</EquationSource> </InlineEquation>-symmetric coefficients, where <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1171_Article_IEq5.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(n&gt;1\)</EquationSource> </InlineEquation>. We study the localizations of the Bloch eigenvalues and the structure of the spectrum. Moreover, we find conditions on the norm of the coefficients under which the spectrum of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1171_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(L\)</EquationSource> </InlineEquation> is purely real and coincides with the real line. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Spectrum of the Differential Operators of Odd Order with \(\mathcal{PT}\)-Symmetric Coefficients

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • Oktay Veliev

摘要

Abstract

In this paper, we consider the Bloch eigenvalues and spectrum of the non-self-adjoint differential operator \(L\) generated by the differential expression of odd order \(n\) with periodic \(\mathcal{PT}\) -symmetric coefficients, where \(n>1\) . We study the localizations of the Bloch eigenvalues and the structure of the spectrum. Moreover, we find conditions on the norm of the coefficients under which the spectrum of \(L\) is purely real and coincides with the real line.