Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I

Details Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I

2008-09-04

arxiv.org/abs/0809.0925v2

Mathematics

Analysis of PDEs

44 pages, 2 figures -- Some explanations, references added; changed normalization of index sets in full calculus to make it mo

Scientific paper

This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior of a manifold with boundary, where the boundary has the structure of a tower of fibre bundles. The class of operators we consider on such a space includes those arising naturally from metrics which degenerate to various orders at the boundary, in directions given by the tower of fibrations. As well as Q-rank 1 locally symmetric spaces, examples include Ricci-flat metrics on the complement of a divisor in a smooth variety constructed by Tian and Yau. In this first part of the calculus construction, parametrices are found for "fully elliptic differential \bfa-operators", which are uniformly elliptic operators on these manifolds that satisfy an additional invertibility condition at infinity. In the second part we will consider operators that do not satisfy this condition.

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