Tauberian Korevaar
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Publication:6401584
DOI10.1016/J.INDAG.2022.08.004arXiv2206.04515MaRDI QIDQ6401584
Publication date: 9 June 2022
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).
Asymptotic results on counting functions for algebraic and topological structures (11N45) Strong limit theorems (60F15) Biographies, obituaries, personalia, bibliographies (01A70) Large deviations (60F10) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Tauberian theorems (40E05) History of sequences, series, summability (40-03)
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