Holomorphic functional calculus of Hodge-Dirac operators in L
p |
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Authors: | Tuomas Hyt?nen Alan McIntosh Pierre Portal |
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Institution: | 1. Department of Mathematics and Statistics, University of Helsinki, Gustaf H?llstr?min katu 2b, FI-00014, Helsinki, Finland 2. Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, 0200, Australia 3. Universit?? Lille 1, Laboratoire Paul Painlev??, 59655, Villeneuve d??Ascq, France
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Abstract: | We study the boundedness of the H
∞ functional calculus for differential operators acting in L
p
(R
n
; C
N
). For constant coefficients, we give simple conditions on the symbols implying such boundedness. For non-constant coefficients,
we extend our recent results for the L
p
theory of the Kato square root problem to the more general framework of Hodge-Dirac operators with variable coefficients
Π
B
as treated in L
2(R
n
; C
N
) by Axelsson, Keith, and McIntosh. We obtain a characterization of the property that Π
B
has a bounded H
∞ functional calculus, in terms of randomized boundedness conditions of its resolvent. This allows us to deduce stability under
small perturbations of this functional calculus. |
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Keywords: | |
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