The Mathematical Intelligencer

, Volume 9, Issue 3, pp 5–7 | Cite as

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Keywords

Piecewise Linear Function Compact Hausdorff Space Uniform Limit Uniform Algebra Weierstrass Theorem 
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References

  1. Abbreviations: Jrb., Zbl.,and MRdenote, respectively, Jahrbuch über die Fortschritte der Mathematik, Zentralblatt für Mathematik,and Mathematical Reviews.Google Scholar
  2. S. N. Bernstein [19121], Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités,Khar’kov, Soobšč. matent, obšč. (2) 13, 1–2.Jrb. 43, 301. Russian translation: Collected works I, 105-106.Google Scholar
  3. —[19122], Sur 1’ ordre de la meilleure approximation des fonctions continues par des polynômes de degré donné,Mém. Acad. Belg. (2) 4, 1–103 (Prize Memoir).Jrb. 43, 493. Also published in Russian in Khar’kov (1912). Collected works I, 11-104.Google Scholar
  4. —[1952-1964], Sobran. soč. (collected works in Russian translation) I,MR 14, 2; II,MR 16, 433; III, MR 23, A32; IV, MR 30, 2. Izdat. Akad. Nauk SSSR, Moscow.Google Scholar
  5. E. Borel [1905], Leçons sur les fonctions de variables réelles et les développements en séries de polynômes, Gauthier-Villars, Paris.Jrb. 36, 435–437. Second edition, 1928.MATHGoogle Scholar
  6. L. deBranges [1959], The Stone-Weierstrass theorem,Proc. Amer. Math. Soc. 10, 822–824.MR 22, 4907.CrossRefMathSciNetGoogle Scholar
  7. P. L. Čebyšev [1853], Théorie des mécanismes connus sous le nom de parallélogrammes,Acad. Imper. Sci. St. Petersburg VII, 539–568; Oeuvres, 109-143.Google Scholar
  8. —[1859], Sur les questions de minima qui se rattachent à la représentation approximative des fonctions,Acad. Imper. Sci. St. Petersburg, Six. série, math, phys., VII, 199–291; Oeuvres, 270-378.Google Scholar
  9. --[1899-1902],Oeuvres, St. Petersburg. Reprinted: Chelsea Pub. Co., New York (1962). MR 26, 4870. Collected works in Russian translation:Poln. sobr. soč. Akad. Nauk SSSR, Vol. 2, 3 (1944-1951).Google Scholar
  10. T. W. Gamelin [1969],Uniform Algebras, Prentice-Hall, Englewood Cliffs,NJ. MR 53, 14137.Google Scholar
  11. Ya. L. Geronimus [1954], P. L. Tschebyschew, Lösung kinematischer Probleme durch Näherungsmethoden, Verlag Technik, Berlin. German translation of one chapter from:Očerk. o rabot, korifeev russ. mek. (Essays on the works of leaders of Russian mechanics),Gos. Izdat. Tehnik-Teoret. Lit., Moscow (1952).MR 15, 275.Google Scholar
  12. D. Jackson [1911], Über die Genauigkeit der Annäherung stetiger Funktionen durch ganze rationale Funktionen gegebenen Grades und trigonometrische Summen gegebener Ordnung, Dissertation, Göttingen (Preisarbeit).Jrb. 42, 434–435.Google Scholar
  13. —[1912], On approximation by trigonometric sums and polynomials,Trans. Amer. Math. Soc. 13 (1912), 491–515.Jrb. 43, 499.CrossRefMATHMathSciNetGoogle Scholar
  14. —[1930], The theory of approximation,Amer. Math. Soc, Colloq. Pub. XI, New York.Jrb. 52, 936.Google Scholar
  15. S. Kakutani [1941], Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.),Ann. of Math. 42, 994–1024.MR 3, 205.CrossRefMATHMathSciNetGoogle Scholar
  16. P. Kirchberger [1902], Über Tschebychefsche Annäherungsmethoden, Dissertation, Göttingen.Jrb. 33, 397–398.Google Scholar
  17. —[1903], Über Tschebychefsche Annäherungsmethoden,Math. Ann. 57, 509–540.Jrb. 34, 438-439.CrossRefMATHMathSciNetGoogle Scholar
  18. I. P. Natanson [1949], Constructive theory of functions,Gos. Izdat. Tehnik-Teoret. Lit., Moscow-Leningrad, 1949 (Russian). MR 11, 591. English translation: F. Ungar. Pub. Co., New York (1955).MR 16, 804.Google Scholar
  19. C. Runge [1884], Zur theorie der eindeutigen analytischen Functionen,Acta Math. 6, 229–244.Jrb. 17, 379-381.CrossRefMathSciNetGoogle Scholar
  20. —[1885], Über die Darstellung willkürlicher Functionen,Acta. Math. 7, 387–392.Jrb. 18, 344-345.CrossRefMathSciNetGoogle Scholar
  21. M. H. Stone [1937], Applications of the theory of Boolean rings to general topology,Trans. Amer. Math. Soc. 41, 375–481.Jrb. 63, 1173;Zbl. 17, 135.CrossRefMathSciNetGoogle Scholar
  22. —[1948], The generalized Weierstrass approximation theorem,Math. Mag. 21, 167–184, 237-254.MR 10, 255.CrossRefMathSciNetGoogle Scholar
  23. K. Weierstrass [1885], Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen einer reellen Veränderlichen,Sitzungsberichte der KoniglichPreussischen Akademie der Wissenschaften zu Berlin (1885), 633-639; 789-805.Jrb. 17, 384-388.Google Scholar

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© Springer Science+Business Media, Inc. 1987

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