Henry Helson meets other big shots -- A brief survey

2019/07/29 by Defant, Andreas, Schoolmann, Ingo
#30550 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A17 #Secondary 30H10

paper · doi:10.48550/arxiv.1907.12323

Abstract

A theorem of Henry Helson shows that for every ordinary Dirichlet series ∑ a_n n^-s with a square summable sequence (a_n) of coefficients, almost all vertical limits ∑ a_n χ(n) n^-s, where χ: ℕ → \mathbbT is a completely multiplicative arithmetic function, converge on the right half-plane. We survey on recent improvements and extensions of this result within Hardy spaces of Dirichlet series -- relating it with some classical work of Bohr, Banach, Carleson-Hunt, Cesàro, Hardy-Littlewood, Hardy-Riesz, Menchoff-Rademacher, and Riemann.

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