| Title:
|
The Weierstrass theorem on polynomial approximation (English) |
| Author:
|
Výborný, Rudolf |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
161-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
approximation by polynomials |
| MSC:
|
41-01 |
| MSC:
|
41A10 |
| idZBL:
|
Zbl 1110.41003 |
| idMR:
|
MR2148649 |
| DOI:
|
10.21136/MB.2005.134132 |
| . |
| Date available:
|
2009-09-24T22:19:36Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134132 |
| . |
| Reference:
|
[1] B. Brosowski, F. Deutsch: An elementary proof of the Stone-Weierstrass theorem.Proc. Am. Math. Soc. 81 (1981), 89–92. MR 0589143, 10.1090/S0002-9939-1981-0589143-8 |
| Reference:
|
[2] D. Jackson: A proof of Weierstrass’s theorem.Am. Math. Mon. 41 (1934), 309–312. Zbl 0009.15802, MR 1523090, 10.2307/2300993 |
| Reference:
|
[3] H. Kuhn: Ein elementarer Beweis des Weierstrasschen Approximationsatzes.Arch. Math. 15 (1964), 316–317. MR 0173738, 10.1007/BF01589203 |
| Reference:
|
[4] E. Landau: Über die Approximationen einer stetigen Funktion durch eine ganze rationale Funktion.Palermo Rend. 25 (1908), 337–345. |
| Reference:
|
[5] I. P. Natanson: Theory of Functions of a Real Variable (Engl. transl.) Vol 1.Ungar, New York, 1974. MR 0354979 |
| Reference:
|
[6] M. H. Stone: A generalized Weierstrass approximation theorem.Stud. Math. 1 (1962), 30–87. Zbl 0147.11702 |
| Reference:
|
[7] Béla Sz.-Nagy: Introduction to Real Functions and Orthogonal Expansions.Akadémiai Kiadó, Budapest, 1964. MR 0181711 |
| Reference:
|
[8] K. Weierstrass: Mathematische Werke.Preussische Akademie der Wissenschaften, 1903. |
| . |
