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<p>Firstly, fundamental properties of the operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(D_{\omega }\)</EquationSource> </InlineEquation> are established, and the decomposition theorem of the polynomial weighted Dirac operator <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(D_{\omega }^{k}\)</EquationSource> </InlineEquation> is given. Secondly, decomposition theorems of polynomial weighted Dirac operators are obtained. Finally, as the applications of the above decomposition theorems, two kinds of generalized Riquier boundary value problems are solved.</p>

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Almansi Decomposition Theorems of Polynomial Weighted Dirac Operators and Their Applications

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Shuoxing He,
  • Yonghong Xie

摘要

Firstly, fundamental properties of the operator \(D_{\omega }\) are established, and the decomposition theorem of the polynomial weighted Dirac operator \(D_{\omega }^{k}\) is given. Secondly, decomposition theorems of polynomial weighted Dirac operators are obtained. Finally, as the applications of the above decomposition theorems, two kinds of generalized Riquier boundary value problems are solved.