Gallardo-Gutiérrez, EA and Partington, JR orcid.org/0000-0002-6738-3216 (2018) C₀-semigroups of 2-isometries and Dirichlet spaces. Revista Matemática Iberoamericana, 34 (3). pp. 1415-1425. ISSN 0213-2230
Abstract
In the context of a theorem of Richter, we establish a similarity between C₀-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C₊ acting boundedly on weighted Dirichlet spaces on C₊. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by Stf(x)={0 if 0≤x≤t,f(x−t) if x>t, acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaces\linebreak of C₀-semigroups of analytic 2-isometries.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 EMS Publishing House. This is an author produced version of a paper published in Revista Matemática Iberoamericana. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | 2-isometries; right-shift semigroups; Dirichlet space |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Apr 2017 10:53 |
Last Modified: | 04 Sep 2018 08:52 |
Status: | Published |
Publisher: | European Mathematical Society |
Identification Number: | 10.4171/RMI/1030 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115266 |