Admissible Functions for the Positive Octant

In this paper, we give examples of admissible functions for the positive octant, which are multidimensional generalizations of regularly varying functions of a single variable introduced by J. Karamata in 1930. For an arbitrary closed convex acute solid $n$-dimensional cone, admissible functions were introduced by Yu. N. Drozhzhinov and B. I. Zav'yalov in 1984 in connection with applications to Tauberian theory and mathematical physics. Results in the asymptotics of multidimensional infinitely divisible distribution laws at infinity were obtained by the author in 2003 by applying admissible functions of the cone.