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<p>One says that an approximation theorem holds for a homogeneous convolution-type equation if any solution of this equation can be approximated by its elementary solutions. In this paper, we state a&#xa0;necessary and sufficient condition for the validity of the approximation theorem for the homogeneous equation of three-way convolution for any choice of a convex domain and its characteristic function.</p>

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SYNTHESIS IN THE KERNEL OF THE THREE-SIDED CONVOLUTION OPERATOR

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. A. Tatarkin,
  • A. B. Shishkin

摘要

One says that an approximation theorem holds for a homogeneous convolution-type equation if any solution of this equation can be approximated by its elementary solutions. In this paper, we state a necessary and sufficient condition for the validity of the approximation theorem for the homogeneous equation of three-way convolution for any choice of a convex domain and its characteristic function.