## Elliptic differential operators on noncompact manifolds.(English)Zbl 0615.58048

The authors study, on a noncompact manifold with a finite number of ends, elliptic differential operators which have a well-defined limit at each infinity. They also determine how the index of the operator changes as the weighting is varied. In the first part of the paper only noncompact manifolds with a single end are studied. The Fredholm property is derived using standard techniques. The index formulas are obtained using multiple-layer potentials and asymptotic expansions. In the second part the authors give some applications of the first part. They generalize the results to manifolds with multiple ends, allowing for different weights on different ends. Next, they consider Douglis-Nirenberg systems on $${\mathbb{R}}^ n$$. Finally, they apply their results to the $$L^ 2$$ Hodge theory for manifolds with conic singularities.
Reviewer: D.Yang

### MSC:

 58J99 Partial differential equations on manifolds; differential operators
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### References:

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