The Weierstrass theorem on polynomial approximation

Rudolf Výborný

Mathematica Bohemica (2005)

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

Abstract

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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

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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

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  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) 

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