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Title: Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I.
Authors: Grieser, Daniel
Hunsicker, Eugenie
Keywords: Pseudodifferential operators
Analysis on locally symmetric spaces
Analysis on singular spaces
Issue Date: 2009
Publisher: © Elsevier Inc.
Citation: 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.
Abstract: This 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.
Description: 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-license
Version: Published
DOI: 10.1016/j.jfa.2009.09.016,
URI: https://dspace.lboro.ac.uk/2134/17170
Publisher Link: http://dx.doi.org/10.1016/j.jfa.2009.09.016,
ISSN: 0022-1236
Appears in Collections:Published Articles (Maths)

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