Comptes Rendus
no. 11-12
Mathematical Analysis/Harmonic Analysis
The Fourier–Stieltjes transform of Minkowskiʼs ?(x) function and an affirmative answer to Salemʼs problem
[La transforme de Fourier–Stieltjes de la fonction ?(x) de Minkowski et une réponse positive au probléme de Salem]

Présenté par : the Editorial Board

Semyon Yakubovich1
1 Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007 Porto, Portugal
Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 633-636.
est référencé par Corrigendum to the Note “The Fourier–Stieltjes transform of Minkowskiʼs ?(x) function and an affirmative answer to Salemʼs problem” [C. R. Acad. Sci. Paris, Ser. I 349 (11–12) (2011) 633–636]

By using structural and asymptotic properties of the Kontorovich–Lebedev transform associated with Minkowskiʼs question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943) 439) whether its Fourier–Stieltjes transform vanishes at infinity.

Grace à des propriétés structurelles et asymptotiques de la transformation de Kontorovich–Lebedev associé à la fonction point dʼinterrogation de Minkowski, on apporte une réponse positive à la question posée par R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943) 439) : la transformée de Fourier–Stieltjes de la fonction point dʼinterrogation de Minkowski est-elle nulle à lʼinfini ?

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.04.004

Semyon Yakubovich 1

1 Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007 Porto, Portugal 
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Semyon Yakubovich. The Fourier–Stieltjes transform of Minkowskiʼs $ ?(x)$ function and an affirmative answer to Salemʼs problem. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 633-636. doi : 10.1016/j.crma.2011.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.004/

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  • Semyon Yakubovich On the affirmative solution to Salem's problem, Analysis (München), Volume 39 (2019) no. 4, pp. 135-149 | DOI:10.1515/anly-2019-0026 | Zbl:1431.42011
  • Elena P. Golubeva Salem's problem for the inverse Minkowski ?(t) function, Journal of Mathematical Sciences (New York), Volume 207 (2015) no. 6, pp. 808-814 | DOI:10.1007/s10958-015-2404-7 | Zbl:1369.11051
  • Semyon Yakubovich On some Rajchman measures and equivalent Salem's problem, Communications in Mathematical Analysis, Volume 14 (2013) no. 1, pp. 28-41 | Zbl:1277.33004
  • Giedrius Alkauskas The Minkowski ?(x) function and Salem's problem, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 350 (2012) no. 3-4, pp. 137-140 | DOI:10.1016/j.crma.2012.01.012 | Zbl:1247.11011

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