The Weierstrass theorem on polynomial approximation

Rudolf Výborný

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 2, page 161-166
  • ISSN: 0862-7959

Abstract

top
In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.

How to cite

top

Výborný, Rudolf. "The Weierstrass theorem on polynomial approximation." Mathematica Bohemica 130.2 (2005): 161-166. <http://eudml.org/doc/249595>.

@article{Výborný2005,
abstract = {In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.},
author = {Výborný, Rudolf},
journal = {Mathematica Bohemica},
keywords = {approximation by polynomials},
language = {eng},
number = {2},
pages = {161-166},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Weierstrass theorem on polynomial approximation},
url = {http://eudml.org/doc/249595},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Výborný, Rudolf
TI - The Weierstrass theorem on polynomial approximation
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 2
SP - 161
EP - 166
AB - In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.
LA - eng
KW - approximation by polynomials
UR - http://eudml.org/doc/249595
ER -

References

top
  1. 10.1090/S0002-9939-1981-0589143-8, Proc. Am. Math. Soc. 81 (1981), 89–92. (1981) MR0589143DOI10.1090/S0002-9939-1981-0589143-8
  2. 10.2307/2300993, Am. Math. Mon. 41 (1934), 309–312. (1934) Zbl0009.15802MR1523090DOI10.2307/2300993
  3. 10.1007/BF01589203, Arch. Math. 15 (1964), 316–317. (1964) MR0173738DOI10.1007/BF01589203
  4. Über die Approximationen einer stetigen Funktion durch eine ganze rationale Funktion, Palermo Rend. 25 (1908), 337–345. (1908) 
  5. Theory of Functions of a Real Variable (Engl. transl.) Vol 1, Ungar, New York, 1974. (1974) MR0354979
  6. A generalized Weierstrass approximation theorem, Stud. Math. 1 (1962), 30–87. (1962) Zbl0147.11702
  7. Introduction to Real Functions and Orthogonal Expansions, Akadémiai Kiadó, Budapest, 1964. (1964) MR0181711
  8. Mathematische Werke, Preussische Akademie der Wissenschaften, 1903. (1903) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.