Orateur
Description
In this talk, I will present an ongoing work whose purpose is to develop a general new method to transfer properties of a linear operator to another. The initial idea was to transfer a Runge approximation property from the Laplace operator to the Stokes operator, by proceeding in several stages, transferring information back and forth by the means of $3$ identities, which involve auxiliary operators which are all local. Yet, it turned out that such a strategy can be extended to the transfer of various properties, such as Fredholmness, local solvability, hypoellipticity, unique continuation and controllability. We will see how categorical language may describe, in a unified way, such transfers, by identifying auxiliary operators, involved in combinations of up to $6$ specific identities, as morphisms between two given operators. Such "transfer categories" can then be tailored to different contexts and needs in algebra, functional analysis, and PDEs.
