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Spectral theory of invariant operators, sharp inequalities, and representation theory. (English) Zbl 0884.58100
Slovák, Jan (ed.), Proceedings of the 16th Winter School on geometry and physics, Srní, Czech Republic, January 13–20, 1996. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 46, 29-54 (1997).
The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.
For the entire collection see [Zbl 0866.00050].

58J70 Invariance and symmetry properties for PDEs on manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J52 Determinants and determinant bundles, analytic torsion