JOURNAL ARTICLE

Approximating Lipschitz and continuous functions by polynomials; Jackson's theorem.

  • Published In: Mathematical Gazette, 2023, v. 107, n. 569. P. 273 1 of 3

  • Database: Mathematics Source 2 of 3

  • Authored By: Jameson, G. J. O. 3 of 3

Abstract

The celebrated theorem of Weierstrass, dating from 1885, states that continuous functions can be uniformly approximated by polynomials on any bounded, closed interval. But just how well can we approximate by polynomials of a certain degree? Let us introduce some notation to facilitate the discussion. For an interval I (which will usually be), denote by C (I) the space of continuous functions on I , and write for (the notation is often used). Uniform convergence of fn to f (on I) equates to the statement that. Denote by the space of polynomials of degree not more than n. This is a linear subspace of C (I) of dimension n + 1. We write [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Mathematical Gazette. 2023/07, Vol. 107, Issue 569, p273
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2023
  • ISSN:0025-5572
  • DOI:10.1017/mag.2023.58
  • Accession Number:164690418
  • Copyright Statement:Copyright of Mathematical Gazette is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.