# The Weierstrass theorem on polynomial approximation

Mathematica Bohemica (2005)

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

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topVýborný, 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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- 10.1007/BF01589203, Arch. Math. 15 (1964), 316–317. (1964) MR0173738DOI10.1007/BF01589203
- Über die Approximationen einer stetigen Funktion durch eine ganze rationale Funktion, Palermo Rend. 25 (1908), 337–345. (1908)
- Theory of Functions of a Real Variable (Engl. transl.) Vol 1, Ungar, New York, 1974. (1974) MR0354979
- A generalized Weierstrass approximation theorem, Stud. Math. 1 (1962), 30–87. (1962) Zbl0147.11702
- Introduction to Real Functions and Orthogonal Expansions, Akadémiai Kiadó, Budapest, 1964. (1964) MR0181711
- Mathematische Werke, Preussische Akademie der Wissenschaften, 1903. (1903)

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