Problèmes de Cauchy hyperboliques en dimension infinie
Problemi inversi, equazioni quasilineari e semigruppi analitici
Propagation des singularités différentiables pour des opérateurs différentiels à coefficients analytiques
Propagation of singularities and maximal functions in the plane.
Propagation of Singularities for Non Real Pseudo-Differential Operators
Properties of eigenfunctions of non-local operators
Pseudodifferential analysis on continuous family groupoids.
Pseudodifferential Operators
Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions
Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem...
Pseudodifferential operators on non-quasianalytic classes of Beurling type
We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class . We also...
Pseudo-spectrum for a class of semi-classical operators
We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some ‘almost eigenvalues’ in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove...
Pseudospectrum for differential operators
Quantification relativiste
Quelques exemples d'opérateurs pseudodifférentiels localement résolubles
Quelques résultats d'existence et régularité pour un problème non linéaire de la théorie du contrôle
Rate of convergence on the mixed summation integral type operators.
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Recent development in the theory of linear partial differential equations.
Reduction of operator families to integral form.
Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Condition.