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On considère des opérateurs à caractéristiques de multiplicité constante et à partie principale réelle. Avec une hypothèse, dite condition de Lévi, sur les termes d’ordre inférieur, on étend à ces opérateurs le théorème de Duistermaat-Hörmander sur l’invariance par le flot hamiltonien du spectre singulier des solutions de . Un point essentiel réside dans la preuve de l’invariance de la condition de Lévi par transformation canonique. On donne une application à la résolubilité locale de ce type...
For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions...
A quasiharmonic field is a pair of vector fields satisfying , , and coupled by a distorsion inequality. For a given , we construct a matrix field such that . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
On considère un polynôme , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégralesdonne des renseignements sur les racines du polynômes de Bernstein de . La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.
In this work we consider two partial differential operators, define a generalized Radon transform and its dual associated with these operators and characterize its range.
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