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A FOURIER-TYPE CHARACTERISATION FOR GEVREY VECTORS ON HYPO-ANALYTIC STRUCTURES AND PROPAGATION OF GEVREY SINGULARITIES

Part of: General first-order equations and systems Miscellaneous topics - Partial differential equations Overdetermined systems

Published online by Cambridge University Press:  07 February 2022

Nicholas Braun Rodrigues Open the ORCID record for Nicholas Braun Rodrigues [Opens in a new window]
Nicholas Braun Rodrigues*
Affiliation:
Universidade Federal de São Carlos (UFSCar) Departamento de Matemática São Carlos, SP 13565-905, Brazil
*
braun.rodrigues@gmail.com
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Abstract

In this work we prove a Fourier–Bros–Iagolnitzer (F.B.I.) characterisation for Gevrey vectors on hypo-analytic structures and we analyse the main differences of Gevrey regularity and hypo-analyticity concerning the F.B.I. transform. We end with an application of this characterisation on a propagation of Gevrey singularities result for solutions of the nonhomogeneous system associated with the hypo-analytic structure for analytic structures of tube type.

Keywords

F.B.I. transformGevrey vectorsHypo-analytic structuresPropagation of singularities

MSC classification

Primary: 35F35: Linear first-order systems
Secondary: 35N10: Overdetermined systems with variable coefficients 35S30: Fourier integral operators
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2177 - 2198
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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