Tauberian Korevaar

Abstract

We focus on the Tauberian work for which Jaap Korevaar is best known, together with its connections with probability theory. We begin (Section 1) with a brief sketch of the field up to Beurling's work. We follow with three sections on Beurling aspects: Beurling slow variation (Section 2); the Beurling Tauberian theorem for which it was developed (Section 3); Riesz means and Beurling moving averages (Section 4). We then give three applications from probability theory: extremes (Section 5), laws of large numbers (Section 6), and large deviations (Section 7). We turn briefly to other areas of Korevaar's work in Section 8. We close with a personal postscript (whence our title).