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Ultradifferential operators in the study of Gevrey solvability and regularity
Author(s) -
Ragognette Luis F.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700393
Subject(s) - mathematics , duality (order theory) , operator (biology) , differential operator , representation (politics) , pure mathematics , class (philosophy) , integrable system , function (biology) , order (exchange) , mathematical analysis , algebra over a field , biochemistry , chemistry , finance , repressor , artificial intelligence , evolutionary biology , politics , biology , political science , transcription factor , computer science , law , economics , gene
In this work we present a new representation formula for ultradistributions using the so‐called ultradifferential operators. The main difference between our representation result and other works is that here we do not break the duality of Gevrey functions of other s and their ultradistributions, i.e., we locally represent an element of D s ′ by an infinite order operator acting on a function of class G s . Our main application was in the local solvability of the differential complex associated to a locally integrable structure in a Gevrey environment.