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<p>In this paper, we obtain the fundamental solution of the polyharmonic Kipriyanov operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta _{B_{-\upgamma }}^m\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow> <msub> <mi>B</mi> <mrow> <mo>-</mo> <mi mathvariant="normal">γ</mi> </mrow> </msub> </mrow> <mi>m</mi> </msubsup> </math></EquationSource> </InlineEquation> with negative parameters of Bessel operators <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((-1&lt;-\upgamma _i&lt;0)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>&lt;</mo> <mo>-</mo> <msub> <mi mathvariant="normal">γ</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where <i>m</i> is a natural number.</p>

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ON THE FUNDAMENTAL SOLUTION OF THE K-POLYHARMONIC OPERATOR

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • E. A. Gryazneva

摘要

In this paper, we obtain the fundamental solution of the polyharmonic Kipriyanov operator \(\Delta _{B_{-\upgamma }}^m\) Δ B - γ m with negative parameters of Bessel operators \((-1<-\upgamma _i<0)\) ( - 1 < - γ i < 0 ) , where m is a natural number.