The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem

• Autorzy: Raymond Mortini
• Języki publikacji: EN

Abstrakty

EN

Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.

Słowa kluczowe

EN

Boundary behaviour of analytic functions; trigonometric series

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2017
• Tom: 71
• Numer: 1

Daty

wydano

2017

online

2017-06-30

Twórcy

autor

Raymond Mortini

Bibliografia

• Cima, J., Ross, W., The Backward Shift on the Hardy Space, AMS, Providence, 2000.
• Fatou, P., Series trigonometriques et series de Taylor, Acta Math. 30 (1906), 335-400.
• Kechris, A. S., Set theory and uniqueness for trigonometric series, Preprint 1997. http://www.math.caltech.edu/ kechris/papers/uniqueness.pdf
• Riesz, F., Riesz, M., Uber die Randwerte einer analytischen Funktion, Quatrieme Congres des Math. Scand. (1916), 27-44,
• Lusin, N., Privaloff, J., Sur l’unicite et la multiplicite des fonctions analytiques, Ann. Sci. ENS 42 (1925), 143-191.
• Rudin, W., Real and Complex Analysis, third edition, McGraw-Hill, New York, 1986.
• Zygmund, A., Trigonometric Series, second edition, Vol. I+II Combined, Cambridge Math. Lib. 1959 and 1993.

Identyfikatory

DOI

10.17951/a.2017.71.1.73