Perturbation of sectorial projections of elliptic pseudo-differential operators

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

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TidsskriftJournal of Pseudo-Differential Operators and Applications
Vol/bind3
Udgave nummer1
Sider (fra-til)49–79
Antal sider31
ISSN1662-9981
DOI
StatusUdgivet - 2012

Bibliografisk note

førhen (2011) arXiv og netpublikation/doi

Citer dette

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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 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.",
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Perturbation of sectorial projections of elliptic pseudo-differential operators. / Booss-Bavnbek, Bernhelm; Chen, Guoyuan; Lesch, Matthias; Zhu, Chaofeng.

I: Journal of Pseudo-Differential Operators and Applications, Bind 3, Nr. 1, 2012, s. 49–79.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer 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.

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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 -