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

Raymond Mortini

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2017)

  • Volume: 71, Issue: 1
  • ISSN: 0365-1029

Abstract

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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.

How to cite

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Raymond Mortini. "The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 71.1 (2017): null. <http://eudml.org/doc/289827>.

@article{RaymondMortini2017,
abstract = {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.},
author = {Raymond Mortini},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Boundary behaviour of analytic functions; trigonometric series},
language = {eng},
number = {1},
pages = {null},
title = {The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem},
url = {http://eudml.org/doc/289827},
volume = {71},
year = {2017},
}

TY - JOUR
AU - Raymond Mortini
TI - The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
IS - 1
SP - null
AB - 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.
LA - eng
KW - Boundary behaviour of analytic functions; trigonometric series
UR - http://eudml.org/doc/289827
ER -

References

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

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