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$ H^\infty$-calculus for the sum of non-commuting operators

Authors: Jan Prüss and Gieri Simonett
Journal: Trans. Amer. Math. Soc. 359 (2007), 3549-3565
MSC (2000): Primary 47A60, 47N20, 35K20
Published electronically: March 20, 2007
MathSciNet review: 2302505
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Abstract: A recent result of Kalton and Weis is extended to the case of non-commuting operators, employing the commutator condition of Labbas and Terreni, or of Da Prato and Grisvard. Under appropriate assumptions it is shown that the sum of two non-commuting operators admits an $ \mathcal H^\infty$-calculus. The main results are then applied to a parabolic problem on a wedge domain.

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Additional Information

Jan Prüss
Affiliation: Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-60120 Halle, Germany

Gieri Simonett
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

Received by editor(s): December 28, 2003
Published electronically: March 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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