1-s2.0-S0022123609003863-main.pdf (521.89 kB)
Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I.
journal contribution
posted on 2015-04-01, 11:14 authored by Daniel Grieser, Eugenie HunsickerThis paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on QQ-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 QQ-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 a-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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Functional AnalysisVolume
257Issue
12Pages
3748 - 3801Citation
GRIESER, D. and HUNSICKER, E., 2009. Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I. Journal of Functional Analysis, 257 (12), pp. 3748 - 3801.Publisher
© Elsevier Inc.Version
- VoR (Version of Record)
Publication date
2009Notes
This article was published in the Journal of Functional Analysis [© Elsevier Inc.]. It is published as an Open Archive article under an Elsevier User Licence, details are available at:http://www.elsevier.com/about/open-access/open-access-policies/oa-license-policy/elsevier-user-licenseISSN
0022-1236Publisher version
Language
- en