Scholarlink

Abstract <p> It is shown that any continuous function depending on several <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic variables, each of which is defined on the ring of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic integers <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Z}_{p}\)</EquationSource> </InlineEquation>, can be represented as a superposition of continuous functions of one <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic variable. This statement is true for both functions with values in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{R}\)</EquationSource> </InlineEquation> and functions with values in <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1128_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Q}_{p}\)</EquationSource> </InlineEquation>. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Analog of the Kolmogorov-Arnold Superposition Representation for Continuous Functions of Several \(p\)-Adic Variables

  • 期刊论文

  • 发表日期：

    2025年8月1日

查看全文
  • A. P. Zubarev

摘要

Abstract

It is shown that any continuous function depending on several \(p\) -adic variables, each of which is defined on the ring of \(p\) -adic integers \(\mathbb{Z}_{p}\) , can be represented as a superposition of continuous functions of one \(p\) -adic variable. This statement is true for both functions with values in \(\mathbb{R}\) and functions with values in \(\mathbb{Q}_{p}\) .