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Abstract <p> The <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation>-hyperbolic operator <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Box _{\gamma }={\partial^2}/{\partial t^2}-a^2 \Delta _{B_{\gamma }}\)</EquationSource> </InlineEquation> is considered with the operator <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Delta _{B_{\gamma }}=\sum_{i=1}^n B_{\gamma _i}\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(B_{\gamma _i}\)</EquationSource> </InlineEquation> are Bessel operators with parameters<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\gamma _i&gt;-1\)</EquationSource> </InlineEquation>. The definition of the <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\delta _{-\gamma }\)</EquationSource> </InlineEquation>-Dirac distribution is introduced, and a formula forthe Bessel transform of the <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\delta _{-\gamma }\)</EquationSource> </InlineEquation>-Dirac distribution is obtained. Three types of fundamental solutions of the <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation>-hyperbolic operator are given. A solution of theinhomogeneous <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation>-hyperbolic equation is presented.</p>

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Fundamental Solution of a \(B \)-Hyperbolic Equation with Negative Parameters

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • L. N. Lyakhov,
  • Yu. N. Bulatov

摘要

Abstract

The \(B\) -hyperbolic operator \(\Box _{\gamma }={\partial^2}/{\partial t^2}-a^2 \Delta _{B_{\gamma }}\) is considered with the operator \(\Delta _{B_{\gamma }}=\sum_{i=1}^n B_{\gamma _i}\) , where \(B_{\gamma _i}\) are Bessel operators with parameters \(\gamma _i>-1\) . The definition of the \(\delta _{-\gamma }\) -Dirac distribution is introduced, and a formula forthe Bessel transform of the \(\delta _{-\gamma }\) -Dirac distribution is obtained. Three types of fundamental solutions of the \(B\) -hyperbolic operator are given. A solution of theinhomogeneous \(B\) -hyperbolic equation is presented.