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**Elliptic theory of differential edge operators. I.**
*(English)*
Zbl 0745.58045

The paper is concerned with the analysis of general elliptic edge operators with constant indicial roots. This includes Laplacians on asymptotically flat and asymptotically hyperbolic manifolds. Edge operators also arise in boundary problems around higher codimension boundaries. In the first part operators which are semi-Fredholm are studied. It is proved that any element of the nullspace of such an operator has a distributional asymptotic expansion. Conditions are given to guarantee that the coefficients of this expansion are smooth. The results are proved using pseudodifferential operators which incorporate the degeneracies of the edge operators.

Reviewer: J.Marschall

### MSC:

58J05 | Elliptic equations on manifolds, general theory |

58J32 | Boundary value problems on manifolds |

58J40 | Pseudodifferential and Fourier integral operators on manifolds |

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\textit{R. Mazzeo}, Commun. Partial Differ. Equations 16, No. 10, 1615--1664 (1991; Zbl 0745.58045)

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