TY - JOUR
T1 - Limit-periodic arithmetical functions and the ring of finite integral adeles
AU - Duy, Trinh Khanh
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/9
Y1 - 2011/9
N2 - In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.
AB - In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.
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U2 - 10.1007/s10986-011-9143-3
DO - 10.1007/s10986-011-9143-3
M3 - Article
AN - SCOPUS:83355169570
SN - 0363-1672
VL - 51
SP - 486
EP - 506
JO - Lithuanian Mathematical Journal
JF - Lithuanian Mathematical Journal
IS - 4
ER -