Scholarlink

<p>The half-line Dirac operators with <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation>-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation>-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> <EquationSource Format="TEX">$\delta $</EquationSource> </InlineEquation>-interactions on a half-lattice in terms of the Schur’s algorithm for analytic functions.</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

Direct and Inverse Spectral Continuity for Dirac Operators

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月9日

查看全文
  • R. V. Bessonov,
  • P. V. Gubkin

摘要

The half-line Dirac operators with L 2 $L^{2}$ -potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general L 2 $L^{2}$ -case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with δ $\delta $ -interactions on a half-lattice in terms of the Schur’s algorithm for analytic functions.