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Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems

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Melbourne, Ian, Paviato, Nicolo and Terhesiu, Dalia (2022) Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems. Israel Journal of Mathematics, 247 . pp. 987-991. doi:10.1007/s11856-021-2273-3

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Abstract

We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral gap. Such a space cannot be embedded in a Hölder space with Hölder exponent greater than ½ unless it consists entirely of coboundaries.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Lipschitz spaces, Function spaces , Dynamics
Journal or Publication Title: Israel Journal of Mathematics
Publisher: Magnes Press
ISSN: 0021-2172
Official Date: April 2022
Dates:
DateEvent
April 2022Published
24 December 2021Available
7 April 2021Accepted
Volume: 247
Page Range: pp. 987-991
DOI: 10.1007/s11856-021-2273-3
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-021-2273-3
Access rights to Published version: Restricted or Subscription Access
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