Denjoy–Luzin theorem: Difference between revisions
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*{{Citation | last1=Denjoy | first1=Arnaud | title=Sur l'absolue convergence des séries trigonométriques | url=http://gallica.bnf.fr/ark:/12148/bpt6k31089/f141 | year=1912 | journal= C.R. Acad. Sci. | volume=155 | pages=135–136}} |
*{{Citation | last1=Denjoy | first1=Arnaud | title=Sur l'absolue convergence des séries trigonométriques | url=http://gallica.bnf.fr/ark:/12148/bpt6k31089/f141 | year=1912 | journal= C.R. Acad. Sci. | volume=155 | pages=135–136}} |
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*{{eom|id=Denjoy–Luzin_theorem}} |
*{{eom|id=Denjoy–Luzin_theorem}} |
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*{{Citation | last1=Luzin | first1=N. N. | title=On the convergence of trigonometric series | language=Russian | id={{JFM|43.0319.03}} | year=1912 | journal=Moskau Math. Samml. | volume=28 | pages=461–472}} |
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[[Category:Fourier series]] |
[[Category:Fourier series]] |
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Revision as of 21:49, 13 February 2012
In mathematics, the Denjoy–Luzin theorem, introduced independently by Denjoy (1912) and Luzin (1912) states that if a trigonometic series converges absolutely on a set of positive measure, then the sum of its coefficients converges absolutely, and in particular the trigonometric series converges absolutely everywhere.
References
- Denjoy, Arnaud (1912), "Sur l'absolue convergence des séries trigonométriques", C.R. Acad. Sci., 155: 135–136
- "Denjoy–Luzin_theorem", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
- Luzin, N. N. (1912), "On the convergence of trigonometric series", Moskau Math. Samml. (in Russian), 28: 461–472, JFM 43.0319.03