On a theorem by Treves

On the Treves theorem for the AKNS equation

According to a theorem of Treves [11], the conserved functionals of the AKNS equation vanish on all pairs of formal Laurent series (q̃, r̃) of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of Bäcklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other p...

Proof of the Treves theorem on the KdV hierarchy

L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute reproduction en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute c...

The Baouendi-treves Approximation Theorem for Continuous Vector Fields

This article establishes the Baouendi-Treves approximation theorem for locally integrable structures whose vector fields have continuous coefficients. As a consequence, some uniqueness results are derived.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Alessandro TREVES

The CA3 and CA1 fields of the mammalian hippocampus are strikingly different in their network architecture: massively recurrent the former, essentially feed-forward the latter. The functional significance of this structural differentiation is not clear, in that neural activity in the two fields shows qualitatively similar features, and computational models generally succeed in mimicking hippoca...