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Abstract <p>The problem of constructing special mean functions that are used to study differential equations with singular differential Bessel operators with negative parameters <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8423_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma_{i}\in(-1,0)\)</EquationSource> <!--LobJMat2560854Lyakhov-m5--> </InlineEquation> is considered. The main theorems on the approximation of functions by their mean values are proved. Constructions of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8423_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta\)</EquationSource> <!--LobJMat2560854Lyakhov-m6--> </InlineEquation>-shaped sequences in weighted linear forms are given. Generalized B-derivatives are constructed, their uniqueness and main properties necessary for studying solutions of linear singular differential equations with Bessel operators with parameters <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8423_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma_{i}\in(-1,0)\)</EquationSource> <!--LobJMat2560854Lyakhov-m7--> </InlineEquation> are proved.</p>

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Generalized \(\boldsymbol{B}\)-Derivatives with Negative Parameter of the Bessel Operator and Mean Functions Generated by the Generalized \(\boldsymbol{\mathbb{T}}\)-Pseudoshift

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • L. N. Lyakhov,
  • S. A. Roshchupkin,
  • Yu. N. Bulatov,
  • E. L. Sanina

摘要

Abstract

The problem of constructing special mean functions that are used to study differential equations with singular differential Bessel operators with negative parameters \(\gamma_{i}\in(-1,0)\) is considered. The main theorems on the approximation of functions by their mean values are proved. Constructions of \(\delta\) -shaped sequences in weighted linear forms are given. Generalized B-derivatives are constructed, their uniqueness and main properties necessary for studying solutions of linear singular differential equations with Bessel operators with parameters \(\gamma_{i}\in(-1,0)\) are proved.