Perturbation of sectorial projections of elliptic pseudo-differential operators

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

Research output: Contribution to journalJournal articleResearchpeer-review

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.
Original languageEnglish
JournalJournal of Pseudo-Differential Operators and Applications
Volume3
Issue number1
Pages (from-to)49–79
Number of pages31
ISSN1662-9981
DOIs
Publication statusPublished - 2012

Cite this

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title = "Perturbation of sectorial projections of elliptic pseudo-differential operators",
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 Calder{\'o}n 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.",
author = "Bernhelm Booss-Bavnbek and Guoyuan Chen and Matthias Lesch and Chaofeng Zhu",
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Perturbation of sectorial projections of elliptic pseudo-differential operators. / Booss-Bavnbek, Bernhelm; Chen, Guoyuan; Lesch, Matthias; Zhu, Chaofeng.

In: Journal of Pseudo-Differential Operators and Applications, Vol. 3, No. 1, 2012, p. 49–79.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Perturbation of sectorial projections of elliptic pseudo-differential operators

AU - Booss-Bavnbek, Bernhelm

AU - Chen, Guoyuan

AU - Lesch, Matthias

AU - Zhu, Chaofeng

N1 - førhen (2011) arXiv og netpublikation/doi

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1007/s11868-011-0042-5

DO - 10.1007/s11868-011-0042-5

M3 - Journal article

VL - 3

SP - 49

EP - 79

JO - Journal of Pseudo-Differential Operators and Applications

JF - Journal of Pseudo-Differential Operators and Applications

SN - 1662-9981

IS - 1

ER -