# Perturbation of sectorial projections of elliptic pseudo-differential operators

Bernhelm Booss-Bavnbek, Guoyuan Chen, Matthias Lesch, Chaofeng Zhu

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## Abstract

Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We showthat it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology whichwe explicitly describe. Our main application deals with a continuous curve of arbitrary first order linear elliptic differential operators over a compact manifold with boundary. Under the additional assumption of the weak inner unique continuation property, we derive the continuity of a related curve of Calderón projections and hence of the Cauchy data spaces of the original operator curve. In the Appendix, we describe a topological obstruction against a verbatim use of R. Seeley’s original argument for the complex powers, which was seemingly overlooked in previous studies of the sectorial projection.
Originalsprog Engelsk Journal of Pseudo-Differential Operators and Applications 3 1 49–79 31 1662-9981 https://doi.org/10.1007/s11868-011-0042-5 Udgivet - 2012

### Bibliografisk note

førhen (2011) arXiv og netpublikation/doi