The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem

Details The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem

2011-03-21

arxiv.org/abs/1103.3979v2

Mathematics

Classical Analysis and ODEs

This paper has been withdrawn by the author, because the main result is based on Naylor's asymptotic formula for the Kontorovi

Scientific paper

By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc., 53 (3), (1943), p. 439) whether its Fourier-Stieltjes transform vanishes at infinity. This paper is substituted with a correct alternative and affirmative solution of Salem's problem and its generalization for derivatives of any order of the Fourier-Stieltjes transform of the Minkowski'i question mark function. The question is finally solved.

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