Smooth and Gevrey Microlocal Hypoellipticity for a Class of Hypocomplex Tube Structures

2023/11/24 by Nicholas Braun Rodrigues, Rodrigues, Nicholas Braun
Mathematics · #32W10 #35N10 (Primary) 35N15 #35S30 (Secondary) #43A32 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2311.14547

openalex publication_date 2023/11/24 · openalex created_date 2023/11/28 · openalex updated_date 2026/07/28

Abstract

We prove a smooth and Gevrey-s microlocal hypoellipticity result for a system of complex vector fields associated with a real-analytic locally integrable structure of tube type, that is also microlocal hypocomplex. In order to so, we employ the use of a certain partial F.B.I. transform adapted to the locally integrable structure, first introduced by M. S. Baouendi, C. H. Chang and F. Treves, and we prove a microlocal characterization of the smooth and Gevrey-s wave front set in terms of the decay of this partial F.B.I. transform.

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