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The null space of the ¯ -Neumann operator

Lars Hörmander — 2004

Annales de l’institut Fourier

Let Ω be a complex analytic manifold of dimension n with a hermitian metric and C boundary, and let = ¯ ¯ * + ¯ * ¯ be the self-adjoint ¯ -Neumann operator on the space L 0 , q 2 ( Ω ) of forms of type ( 0 , q ) . If the Levi form of Ω has everywhere at least n - q positive or at least q + 1 negative eigenvalues, it is well known that Ker has finite dimension and that the range of is the orthogonal complement. In this paper it is proved that dim Ker = if the range of is closed and the Levi form of Ω has signature ...

Hypoelliptic differential operators

Lars Hörmander — 1961

Annales de l'institut Fourier

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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