Prof. Boulmezaoud, Tahar Zamene, Laboratoire de
Mathématiques de Versailles, Université de Versailles, France

Title: On Fourier transform and weighted Sobolev spaces

Astract: We prove that Fourier transform defines a simple correspondance between weighted Sobolev spaces. As a consequence, we display a chain of nested invariant spaces over which Fourier transform is an isometry.


16:30–17:00 hrs

Prof. Lev Birbrair, Federal Univerisity of Ceara, Brazil

Title: Resonance sequences.  Differential equations meet Number Theory.

Abstract: We will present some combinatorial or number theoretical
problems coming from Geometric Theory of Ordinary Differential Equations
of the Second Order.

17:00—17:10 hrs.  Coffee Break

17:10–17:40 hrs.

 Prof. Huynh Van Ngai, University of Quy Nhon, Vietnam

Title:  Inverse function theorems  for multifunctions in graded Fréchet

Abstract:  The inverse function theorem is one of the central components
of the classical and the modern variational analysis and an essential
device to solving nonlinear equations. The inverse function theorem or
its variants known as the implicit function theorem or the rank theorem
have  been established originally in Euclidean spaces  and then extended
to the Banach space setting. Outside this setting, for instance in
Fréchet spaces, it is known that the inverse function theorem generally
fails. This is the reason why another form of inverse function theorem,
nowadays called the Nash-Moser theorem is used as a powerful tool to
prove local existence for non-linear partial differential equations in
spaces of smooth functions.
Some inverse theorems  of  Nash-Moser type have also  been proved for
functions between Fréchet spaces, that are  supposed to be tame, an
additional  property  guaranteeing that the semi-norms satisfy some
interpolation properties, or that allow the  use of  smoothing operators
as introduced by Nash. To overcome the loss of derivatives, these
additional properties in Fréchet spaces allow Newton’s method on which
the Nash-Moser type inverse function theorems are based to converge.
Recently, Ekeland produced a new result within a class of spaces much
larger than the
one used in the Nash-Moser literature.
In this talk, we present some inverse function theorems and implicit
function theorems for set-valued mappings between Fréchet spaces. The
proof relies on Lebesgue’s Dominated Convergence Theorem and on
Ekeland’s variational principle. An application to the existence of
solutions of differential equations in Fréchet spaces with non-smooth
data is given.

Miércoles 22 de noviembre a las 16:00 hrs, sala de seminarios John Von Neumann CMM, Beauchef 851, Torre Norte, Piso 7.

Date: Nov 22, 2017 at 16:00 h
Venue: Beuchef 851, Torre Norte, Piso 7, Sala de Seminarios John Vob Neumann CMM.
Speaker: Prof. Boulmezaoud, Tahar Zamene, & Prof. Lev Birbrair, & Prof. Huynh Van Ngai.
Affiliation: Université de Versailles, France & Federal Univerisity of Ceara, Brazil & University of Quy Nhon, Vietnam.
Coordinator: Prof. Abderrahim Hantoute

Posted on Nov 20, 2017 in Optimization and Equilibrium, Seminars