Submission date: 5 June 2018

Abstract:

We construct a Hardy field that contains Ilyashenko's class of germs at infinity of almost regular functions as well as all log-exp-analytic germs. In addition, each germ in this Hardy field is uniquely characterized by an asymptotic expansion that is an LE-series as defined by van den Dries et al. As these series generally have support of order type larger than that of the set of natural numbers, the notion of asymptotic expansion itself needs to be generalized.

Mathematics Subject Classification: Primary 26A12, 41A60, 30E15, Secondary 37E35, 03C99

Keywords and phrases: Transserial asymptotic expansions, quasianalyticity, Hardy fields, analysable functions.

Full text arXiv 1806.01732: pdf, ps.