Mathematics – Spectral Theory
Scientific paper
2010-12-30
J. Pseudo-Differ. Oper. Appl. 3 (2012), 49-79
Mathematics
Spectral Theory
30 pages, 2 figures; v3: major revision, shortened, several references added, some material moved into an appendix; v4: final
Scientific paper
10.1007/s11868-011-0042-5
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 show that it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology which we 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 Calderon 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.
Booss-Bavnbek Bernhelm
Chen Guoyuan
Lesch Matthias
Zhu Chaofeng
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