The H-functional calculus

  • Tuomas Hytönen
  • Jan van Neerven
  • Mark Veraar
  • Lutz Weis
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 67)

Abstract

Now that we have a variety of probabilistic and operator-theoretic tools at our disposal it is time to start using them. The present chapter is devoted to the study of sectorial operators (this class of operators includes, e.g., uniformly elliptic second order differential operators) and their holomorphic functional calculus formally defined by the Dunford integral
$$ f\left( A \right) = \frac{1}{2\pi i}\int_{\partial \sum } {f\left( z \right)\left( {z - A} \right)^{ - 1} \text{d}z} . $$

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tuomas Hytönen
    • 1
  • Jan van Neerven
    • 2
  • Mark Veraar
    • 3
  • Lutz Weis
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  3. 3.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  4. 4.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany

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