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f.b.i. transform

Journal of the Institute of Mathematics of Jussieu (1)

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A FOURIER-TYPE CHARACTERISATION FOR GEVREY VECTORS ON HYPO-ANALYTIC STRUCTURES AND PROPAGATION OF GEVREY SINGULARITIES
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Nicholas Braun Rodrigues
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 5 / September 2023

Published online by Cambridge University Press:

07 February 2022, pp. 2177-2198

Print publication:

September 2023
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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.