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Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces

Neyt Lenny (Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Gent, Belgium), lenny.neyt@ugent.be
Vindas Jasson (Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Gent, Belgium), jasson.vindas@ugent.be

We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those ultradistributions satisfying this asymptotic formula in the one-dimensional case. We also introduce and study a uniform variant of the MAE.

Keywords: Asymptotic behavior of generalized functions, moment asymptotic expansions, S-asymptotics, quasiasymptotics, ultradistribution spaces