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

Yakubovich, Semyon1
1 Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007 Porto, Portugal
Comptes Rendus. Mathématique, Tome 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]

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 ?

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.04.004
Yakubovich, Semyon 1

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

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