Jean Martin Paoli

Densité des vecteurs propres généralisés d'une classe d'opérateurs compacts non auto-adjoints et applications

AbstractWe consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence ofξ0 ∈ϱ(T) such thatK = (T -ξ0I)-1 is compact and the existence ofp>0 such thatsn(K)=o((n−1/p)), whereSn(K) denotes the sequence of non-zero eigenvalues of the compact hermitian operator

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

\sqrt {K*K}

Unitary representations of groups, continuity and spectrum

. In this work, sufficient conditions (announced in [1]) are introduced to assure that the closed subspace ofE spanned by the generalized eigenvectors ofT coincides withE. These conditions are in particular verified by a family of non-self-adjoint operators arising in reggeons field theory.

Quelques propriétés de régularité de l'opérateur de Gribov

In this work, we establish new regularity properties for Gribovs operator:H=μA*A+iλA*(A+A*)A;(μ,λ)∈ℝ2, whereA* andA are the creation and annihilation operators. Particularly, we prove that for all ε>0,H−1 is in the class of Carlemans operatorl1+ε.

Spectral properties of continuous representations of topological groups

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a nonconservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary lagrangian eulerian formulation, in order to compute the solution in the moving domain.