2011/03/21 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · Physics and Astronomy · #11A55 #11F03 #26A30 #33C10 #42A38 #44A10 #44A15 #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Statistical Mechanics and Entropy #math.CA #math.CV #math.FA #math.NT #msc:11A55 #msc:11F03 #msc:26A30 #msc:33C10 #msc:42A38 #msc:44A10 #msc:44A15
paper · pdf · doi:10.48550/arxiv.1103.3979
This paper has been withdrawn by the author, because the main result is based on Naylor's asymptotic formula for the Kontorovich-Lebedev transform at infinity, whose proof has a gap for extreme values of a parameter under required continuity condition and needs perhaps more strong condition of analyticity in some sector of complex plane
openalex publication_date 2011/03/21 · arxiv created 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.