Abdelkader Intissar

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

Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation

\sqrt {K*K}

On an unconditional basis of generalized eigenvectors of the nonself-adjoint Gribov operator in Bargmann space

. 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.

On an Riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid

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.

Analyse de Scattering d'un Opérateur Cubique de Heun dans l'Espace de Bargmann

This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.