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<p>In this paper, we construct a discrete weighted <i>h</i>-Hartley-cosine convolution operator on the time scale <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {T}_h\)</EquationSource> </InlineEquation>. We then establish the boundedness of this operator on the space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(l_1(\mathbb {T}_h)\)</EquationSource> </InlineEquation> and prove the associated factorization identities. As an application, we derive <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(l_1(\mathbb {T}_h)\)</EquationSource> </InlineEquation>-solvability results for certain classes of integral equations and systems of integral equations on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb {T}_h\)</EquationSource> </InlineEquation>. In addition, from a signal-processing viewpoint, we interpret the proposed generalized convolution as a discrete filtering mechanism and illustrate it on the ECG5000 dataset.</p>

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Application of the h-Hartley–Cosine Convolution on \(\mathbb {T}_h\) to Integral Equations and Signal Analysis

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Tran Kim Huong,
  • Dang Ba Ty

摘要

In this paper, we construct a discrete weighted h-Hartley-cosine convolution operator on the time scale \(\mathbb {T}_h\) . We then establish the boundedness of this operator on the space \(l_1(\mathbb {T}_h)\) and prove the associated factorization identities. As an application, we derive \(l_1(\mathbb {T}_h)\) -solvability results for certain classes of integral equations and systems of integral equations on \(\mathbb {T}_h\) . In addition, from a signal-processing viewpoint, we interpret the proposed generalized convolution as a discrete filtering mechanism and illustrate it on the ECG5000 dataset.