Nonlinear normalization in Urbanik's convolutions (Q1175844)

The author considers nonlinear normalizations of Urbanik's generalized convolutions, which are introduced by \textit{K. Urbanik} in three articles [Stud. Math. 23, No. 3, 217--245 (1964; Zbl 0171.39504), ibid. 45, 57--70 (1973; Zbl 0283.60017), ibid. 80, 167--189 (1984; Zbl 0561.60019)] and which are cited in the literature list. In the main theorem the author gives a description of the type of nonlinear standardizing functions needed for the existence of a limit in the non regularly merging case. This result generalizes earlier results found in the literature.