Sequential regular variation: extensions of Kendall's theorem

2019/01/21 by Bingham, N. H., Ostaszewski, A. J.
#26A03 #26A12 #33B99 #39B22 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.07060

Abstract

Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is, with sequential rather than continuous limits. This extends the main result, a theorem of Kendall's (which builds on earlier work of Kingman and Croft), to the general setting.

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