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Ilyashenko algebras based on transserial asymptotic expansions

2018/06/05 by Zeinab Galal, Tobias Kaiser, Galal, Zeinab +3
Mathematics · #03C99 #30E15 #41A60 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Logic (math.LO) #Primary 26A12 #Secondary 37E35 #math.CA #math.CV #math.LO #msc:03C99 #msc:26A12 #msc:30E15 #msc:37E35 #msc:41A60

paper · pdf · doi:10.48550/arxiv.1806.01732

67 pages, updated introduction

arxiv created 2019/01/08 · arxiv updated 2019/01/09

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.

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