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Ultradifferential operators in the study of Gevrey solvability and regularity

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  • Luis F. Ragognette

Abstract

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 Ds′ by an infinite order operator acting on a function of class Gs. Our main application was in the local solvability of the differential complex associated to a locally integrable structure in a Gevrey environment.

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  • Luis F. Ragognette, 2019. "Ultradifferential operators in the study of Gevrey solvability and regularity," Mathematische Nachrichten, Wiley Blackwell, vol. 292(2), pages 409-427, February.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:2:p:409-427
    DOI: 10.1002/mana.201700393
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