Abstract
In this final chapter we present a substantial application of the tools developed in the earlier chapters by constructing and characterising the H∞-functional calculus of sectorial and bi-sectorial operators in a Banach space. We begin with a general theory of the sectorial operators and a construction of the H∞-calculus, complemented by several examples. In two sections, we connect the H∞-calculus to R-boundedness on the one hand, and to the generalised square functions on the other hand. In an independent section, we show the necessity of certain assumptions on the underlying Banach space to some of the deeper results about the H∞-calculus. In two final sections, we discuss the H∞-calculus of bi-sectorial operators, and establish the H∞-calculus of generators of appropriate groups and semigroups on UMD spaces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hytönen, T., van Neerven, J., Veraar, M., Weis, L. (2017). The H∞-functional calculus. In: Analysis in Banach Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-319-69808-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-69808-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69807-6
Online ISBN: 978-3-319-69808-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)