Vol. 70, No. 1, 1977

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Remarks on singular elliptic theory for complete Riemannian manifolds

Heinz Otto Cordes and Robert Colman McOwen

Vol. 70 (1977), No. 1, 133–141

This paper is about a C-algebra A of 0-order pseudo-differential operators on L2(Ω), where Ω is a complete Riemannian manifold which need not be compact. This algebra is designed to handle singular elliptic theory for certain N-th-order differential operators. In particular, this paper studies the maximal ideal space M of the (commutative) algebra A𝒦, where 𝒦 denotes the compact ideal. The space M contains the bundle of cospheres as a subspace, and in general will contain additional points at infinity of the manifold. The significance of this for elliptic theory lies in the fact that an operator A A is Fredholm if and only if the associated continuous function σA C(M) is never zero.

Mathematical Subject Classification 2000
Primary: 58G10
Secondary: 46L99
Received: 19 December 1976
Published: 1 May 1977
Heinz Otto Cordes
Robert Colman McOwen