Minkowski问号函数的Fourier-Stieltjes变换与Salem问题的肯定回答
经典分析与常微分方程
2011-12-21 v2 复变函数
泛函分析
数论
摘要
通过利用与Minkowski问号函数相关的Kontorovich-Lebedev变换的结构和渐近性质，我们对R. Salem（Trans. Amer. Math. Soc., 53 (3), (1943), p. 439）提出的问题——其Fourier-Stieltjes变换是否在无穷远处消失——给出了肯定回答。本文给出了Salem问题的一个正确替代性肯定解，并将其推广到Minkowski问号函数的Fourier-Stieltjes变换的任意阶导数。该问题最终得以解决。
引用
@article{arxiv.1103.3979,
title = {The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1103.3979},
year = {2011}
}
备注
This paper has been withdrawn by the author, because the main result is based on Naylor's asymptotic formula for the Kontorovich-Lebedev transform at infinity, whose proof has a gap for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