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<p>In this paper, we study the so called Kato-Rellich theorem. We prove a similar result for multi-subordinate perturbation. Moreover, we apply this result to study a perturbed operator of Nagy and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1244_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(n \times n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> block matrices of linear operators. The obtained results are of importance to be applicated to study the Schrödinger operators. Finally, we give an application to a Gribov operator in Bargmann space.</p>

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On the Kato-Rellich theorem and applications for multi-subordinate perturbations

  • 期刊论文

  • 发表日期：

    2025年1月14日

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  • Abdessattar Lafi

摘要

In this paper, we study the so called Kato-Rellich theorem. We prove a similar result for multi-subordinate perturbation. Moreover, we apply this result to study a perturbed operator of Nagy and \(n \times n\) n × n block matrices of linear operators. The obtained results are of importance to be applicated to study the Schrödinger operators. Finally, we give an application to a Gribov operator in Bargmann space.