A rapid convergence method for a singular perturbation problem
A selfadjoint hyperbolic boundary-value problem.
A spectral problem with an indefinite weight for an elliptic system.
Almost everywhere summability of eigenfunction expansions associated to elliptic operators
Biorthogonality condition for axisymmetric Stokes flow in spherical geometries.
Biorthogonality condition for creeping motion in annular trenches.
Coerciveness inequality for nonlocal boundary value problems for second order abstract elliptic differential equations.
Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain.
Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats
En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.
Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
Controllability of partial differential equations on graphs
We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the heat equation...
Convergence de la métrique de Fubini-Study d'un fibré linéaire positif
Soit , un fibré linéaire positif au-dessus d’une variété complexe compacte. Nous montrons que la fonction de distorsion définie par le rapport entre la métrique initiale et la métrique de Fubini-Study de admet un équivalent lorsque tend vers l’infini. Ceci améliore les encadrements de Kempf et Ji sur les variétés abéliennes, et les étend à toute variété projective. La démonstration repose sur le calcul d’un équivalent pour le noyau de la chaleur, avec contrôle de la convergence par rapport...
Correction "Almost everywhere summability of eiegnfunction expansion associated to elliptic operators" by Waldemar Hebish, Studia Math. 96(3) 1990, 263-275
Eigenfunction Expansions and the Pinksy Phenomenon on Compact Manifolds.
Eigenstructure of the equilateral triangle. II: The Neumann problem.
Eigenstructure of the equilateral triangle. III: The Robin problem.
Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle
A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
Eliciting harmonics on strings
One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at . The 'correct touch' is that b for which the modes, that do not vanish at , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree ....