A Class of Hypoelliptic Pseudodifferential Operators with Double Characteristics.
Let be a complex analytic manifold of dimension with a hermitian metric and boundary, and let be the self-adjoint -Neumann operator on the space of forms of type . If the Levi form of has everywhere at least positive or at least negative eigenvalues, it is well known that has finite dimension and that the range of is the orthogonal complement. In this paper it is proved that dim if the range of is closed and the Levi form of has signature ...
On donne une condition suffisante pour l’hypoellipticité d’une équation différentielle à coefficients variables. La démonstration utilise une paramétrix construite par transformation de Fourier.
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