Structural theorems for quasiasymptotics of ultradistributions

Article type: Research Article

Authors: Neyt, Lenny | Vindas, Jasson^{; *}

Affiliations: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium. E-mails: lenny.neyt@UGent.be, jasson.vindas@UGent.be

Correspondence: [*] Corresponding author. E-mail: jasson.vindas@UGent.be.

Abstract: We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand–Shilov type spaces.

Keywords: Quasiasymptotic behavior, ultradistributions, regularly varying functions

DOI: 10.3233/ASY-181514

Journal: Asymptotic Analysis, vol. 114, no. 1-2, pp. 1-18, 2019