Scholarlink

<p>A snake is a polynomial of degree <i>n</i> whose graph on a given interval lies between two graphs of continuous functions (the corridor) and coincides with each of them at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7936_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((n+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> points, alternating between them. The classical example is the Chebyshev polynomial <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7936_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>. In this paper, a theorem is proven about the exact growth outside the corridor of the moduli of polynomials (and their derivatives) whose graphs are contained within the corridor. Other extremal properties of snake polynomials are also discussed.</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

Extremal Properties of Snake Polynomials

  • 期刊论文

  • 发表日期：

    2025年8月1日

查看全文
  • Roald M. Trigub

摘要

A snake is a polynomial of degree n whose graph on a given interval lies between two graphs of continuous functions (the corridor) and coincides with each of them at \((n+1)\) ( n + 1 ) points, alternating between them. The classical example is the Chebyshev polynomial \(T_{n}\) T n . In this paper, a theorem is proven about the exact growth outside the corridor of the moduli of polynomials (and their derivatives) whose graphs are contained within the corridor. Other extremal properties of snake polynomials are also discussed.