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On an extrapolation problem for characteristic functions
Lithuanian Mathematical Journal ( IF 0.413 ) Pub Date : 2020-05-31 , DOI: 10.1007/s10986-020-09485-7
Saulius Norvidas

Let f be the characteristic function of a probability measure μf on ℝn, and let σ > 0. We study the following extrapolation problem: under what conditions on the neighborhood of infinity Vσ = {x ∈ ℝn : |xk| > σ, k = 1, …n} in ℝndoes there exist a characteristic function g on ℝn, such that g = f on Vσ but g ≢ f? Let μf have a nonzero absolutely continuous part with continuous density 𝜑. In this paper, we give certain sufficient conditions on 𝜑 and Vσ under which the latter question has an affirmative answer. We also address the optimality of these conditions. Our results indicate that not only does the size of both Vσ and the support supp 𝜑 matter, but also certain arithmetic properties of supp 𝜑.
更新日期:2020-07-02

 

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