Extended calculi and powers of operators

Tuomas Hytönen; Jan van Neerven; Mark Veraar; Lutz Weis

doi:10.1007/978-3-031-46598-7_5

Extended calculi and powers of operators

Tuomas Hytönen^*, Jan van Neerven, Mark Veraar, Lutz Weis

^*Corresponding author for this work

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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.

Original language	English
Title of host publication	Ergebnisse der Mathematik und ihrer Grenzgebiete
Publisher	Springer
Pages	419-513
Number of pages	95
DOIs	https://doi.org/10.1007/978-3-031-46598-7_5
Publication status	Published - 2023

Publication series

Name	Ergebnisse der Mathematik und ihrer Grenzgebiete
Volume	76
ISSN (Print)	0071-1136
ISSN (Electronic)	2197-5655

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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Extended calculi and powers of operators

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