Some remarks on Trèves' conjecture

2013/03/15 by Tove Dahn, Dahn, Tove
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.AP

paper · pdf · doi:10.48550/arxiv.1303.3802

arxiv created 2013/03/15 · openalex publication_date 2013/03/15 · arxiv updated 2013/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

I will give a discussion of the conditions involved in Treves' conjecture on analytic hypoellipticity. I will discuss some microlocally characteristic sets and introduce a topology of monotropic functionals as suitable for solving the conjecture. The pseudodifferential operator representation is inspired by Cousin.

Related

• Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture
• (Semi-)Global Analytic Hypoellipticity for a class of "sums of squares" which fail to be locally analytic hypoelliptic
• Relations between different types of Hypoellipticity: A systematic approach
• Hypoellipticity of analytic differential operators in general ultradifferentiable classes
• Failure of analytic hypoellipticity in a class of PDOs