Some remarks on Tr\`eves' conjecture
Tove Dahn
TL;DR
This paper discusses conditions related to Treves' conjecture on analytic hypoellipticity, exploring microlocal characteristic sets and introducing a topology of monotropic functionals to approach the problem.
Contribution
It introduces a topology of monotropic functionals and discusses microlocal characteristic sets, providing new insights towards solving Treves' conjecture.
Findings
Analysis of microlocally characteristic sets
Introduction of monotropic functional topology
Insights into conditions for analytic hypoellipticity
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology