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H ∞-functional calculus and models of Nagy–Foiaş type for sectorial operators

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Abstract

We prove that a sectorial operator admits an H ∞-functional calculus if and only if it has a functional model of Nagy–Foiaş type. Furthermore, we give a concrete formula for the characteristic function (in a generalized sense) of such an operator. More generally, this approach applies to any sectorial operator by passing to a different norm (the McIntosh square function norm). We also show that this quadratic norm is close to the original one, in the sense that there is only a logarithmic gap between them.

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Authors and Affiliations

  1. Departamento de Matemáticas and I. U. M. A., Universidad de Zaragoza, 50009, Zaragoza, Spain

    José E. Galé & Pedro J. Miana

  2. Departamento de Matemáticas, Universidad Autonoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    Dmitry V. Yakubovich

  3. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain

    Dmitry V. Yakubovich

Authors
  1. José E. Galé
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  2. Pedro J. Miana
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  3. Dmitry V. Yakubovich
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Correspondence to José E. Galé.

Additional information

J. E. Galé and P. J. Miana have been supported by Project E-64, Gobierno de Aragón and Projects MTM2004-03036 and MTM2007-61446, DGI-FEDER, of the MCYT, Spain.

D. V. Yakubovich has been supported by the Ramón and Cajal Programme (2002) and the Project MTM2008-06621-C02-01, DGI-FEDER, of the Ministry of Science and Innovation, Spain.

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Galé, J.E., Miana, P.J. & Yakubovich, D.V. H ∞-functional calculus and models of Nagy–Foiaş type for sectorial operators. Math. Ann. 351, 733–760 (2011). https://doi.org/10.1007/s00208-010-0614-3

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  • DOI: https://doi.org/10.1007/s00208-010-0614-3

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