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<p>Mixed-norm is a popular tool in recent years and has received the attention of many mathematicians. In this paper, based on the study of signals in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2412_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{\vec {p}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mover accent="true"> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </msub> </math></EquationSource> </InlineEquation> (mixed-norm) sense, we provide a study on the approximation of signals by interpolation projection operator <i>I</i> in the mixed-norm <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2412_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{\vec {p}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mover accent="true"> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </msub> </math></EquationSource> </InlineEquation> sense. That is to say, specific conclusions on the approximation order of the interpolation projection operator <i>I</i> based on mixed-norm are given. In fact, the non commutativity of integrals in the sense of mixed-norm poses some difficulties in estimating the error bound of approximation, and this is one of the core issues that this paper must address.</p>

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Approximation Estimation of Interpolation Projection Operators in Shift-Invariant Subspaces Based on Mixed-Norm

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • Yasong Chen,
  • Junjian Zhao

摘要

Mixed-norm is a popular tool in recent years and has received the attention of many mathematicians. In this paper, based on the study of signals in the \(L_{\vec {p}}\) L p → (mixed-norm) sense, we provide a study on the approximation of signals by interpolation projection operator I in the mixed-norm \(L_{\vec {p}}\) L p → sense. That is to say, specific conclusions on the approximation order of the interpolation projection operator I based on mixed-norm are given. In fact, the non commutativity of integrals in the sense of mixed-norm poses some difficulties in estimating the error bound of approximation, and this is one of the core issues that this paper must address.