The Fourier–Stieltjes transform of Minkowskiʼs $ ?(x)$ function and an affirmative answer to Salemʼs problem

Semyon Yakubovich

doi:10.1016/j.crma.2011.04.004

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 Yakubovich ¹

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]

Résumé
Abstract

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 : 2011-03-22
Accepté le : 2011-04-11
Publié le : 2011-06-01

DOI : 10.1016/j.crma.2011.04.004

Affiliations des auteurs :

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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     title = {The {Fourier{\textendash}Stieltjes} transform of {Minkowski's} $ ?(x)$ function and an affirmative answer to {Salem's} problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {633--636},
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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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