Extended calculi and powers of operators

Book chapter (2023)

Authors

Tuomas Hytönen Viikki Biocenter 1
J.M.A.M. van Neerven Analysis - EEMCS
M.C. Veraar Analysis - EEMCS
L Weis Karlsruhe Institut für Technologie
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2023 Tuomas Hytönen, J.M.A.M. van Neerven, M.C. Veraar, Lutz Weis
DOI: https://doi.org/10.1007/978-3-031-46598-7_5
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

In this chapter we address two strongly interwoven topics: How to verify the boundedness of the H∞-calculus of an operator and how to represent and estimate its fractional powers. For concrete operators such as the Laplace operator or elliptic partial differential operators, the fractional domain spaces can often be identifed with certain function spaces considered in Chapter 14 and the imaginary powers of the operator are related to singular integral and pseudo-differential operators treated in Chapters 11 and 13.