**Expositores**

**16:00–16:30hrs **

** 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

spaces

**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.

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