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Sharp inequalities, the functional determinant, and the complementary series
Results in the spectral theory of differential operators, and recent results on conformally covariant differential operators and on sharp inequalities, are combined in a study of functionalExpand
Differential operators cononically associated to a conformal structure.
Soit (M,g) une variete pseudoriemannienne de dimension n. On donne des formules explicites pour un operateur d'ordre 4. D 4 ,k sur les k-formes dans M, n¬=1, 2, 4 pour un operateur D6 d'ordre 6 surExpand
Group representations arising from Lorentz conformal geometry
Abstract It is shown that there exist conformally covariant differential operators D 2 l , k of all even orders 2 l , on differential forms of all orders k , in the double cover n of the nExpand
Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere
We derive sharp Moser-Trudinger inequalities on the CR sphere. The rst type is in the Adams form, for powers of the sublaplacian and for general spectrally dened operators on the space ofExpand
Explicit functional determinants in four dimensions
4 2 2 ABSTRACT. Working on the four-sphere S , a flat four-torus, S x S2, or a compact hyperbolic space, with a metric which is an arbitrary positive function times the standard one, we give explicitExpand
Stein–Weiss Operators and Ellipticity
Abstract Stein and Weiss (1968, Am. J. Math. 90 , 163–196) introduced the notion of generalized gradients : equivariant first order differential operators G between irreducible vector bundles withExpand
The asymptotics of the Laplacian on a manifold with boundary
Let P be a second-order differential operator with leading symbol given by the tensor on a compact Riemannian manifold with boundary. We compute the asymptotics of the heat equation for Dirichlet,Expand
Conformally invariant non-local operators
On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) isExpand
Residues of the eta function for an operator of Dirac type
Abstract We compute the asymptotics of Tr L 2 ( Pe −tp 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the eta function.
The Functional determinant
Results in the spectral theory of diierential operators, and recent results on conformally covariant diierential operators and on sharp inequalities, are combined in a study of functionalExpand
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