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<p>In this paper, we delve into the convergence challenges concerning a function <i>f</i> represented as a Fourier series within Sobolev and generalized Zygmund norms. Our approach involves utilizing the deferred Nörlund–deferred Cesàro product (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3284_Article_IEq1.gif" Format="GIF" Height="29" Rendition="HTML" Resolution="72" Type="Linedraw" Width="126" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msubsup> <mi>D</mi> <msub> <mi>h</mi> <mi>μ</mi> </msub> <msub> <mi>d</mi> <mi>μ</mi> </msub> </msubsup> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msup> <mo stretchy="false">)</mo> <msubsup> <mi>D</mi> <msub> <mi>g</mi> <mi>μ</mi> </msub> <msub> <mi>h</mi> <mi>μ</mi> </msub> </msubsup> <mo stretchy="false">(</mo> <mi>C</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$D_{h_{\mu}}^{d_{ \mu}}(N^{p,q})D_{g_{\mu}}^{h_{\mu}}(C)$</EquationSource> </InlineEquation>) means of Fourier series in order to examine this convergence phenomenon. Further, we conduct a comparative analysis of the convergence outcomes through practical validations.</p>

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An analysis of the convergence problem of a function in Sobolev and generalized Zygmund norms using product operator

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  • 发表日期：

    2025年3月24日

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  • H. K. Nigam,
  • Swagata Nandy

摘要

In this paper, we delve into the convergence challenges concerning a function f represented as a Fourier series within Sobolev and generalized Zygmund norms. Our approach involves utilizing the deferred Nörlund–deferred Cesàro product ( D h μ d μ ( N p , q ) D g μ h μ ( C ) $D_{h_{\mu}}^{d_{ \mu}}(N^{p,q})D_{g_{\mu}}^{h_{\mu}}(C)$ ) means of Fourier series in order to examine this convergence phenomenon. Further, we conduct a comparative analysis of the convergence outcomes through practical validations.