Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 4, pp. 509-520   https://doi.org/10.15407/mag17.04.509     ( to contents , go back )
https://doi.org/10.15407/mag17.04.509

One Class of Linearly Growing C0-Groups

Grigory Sklyar

Institute of Mathematics, University of Szczecin, Szczecin, Poland
E-mail: sklar@univ.szczecin.pl

Vitalii Marchenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: v.marchenko@ilt.kharkov.ua

Piotr Polak

Institute of Mathematics, University of Szczecin, Szczecin, Poland
E-mail: piotr.polak@usz.edu.pl

Received August 27, 2021, revised November 23, 2021.

Abstract

We consider special class of C0-groups from [12], whose generators are unbounded, have pure point imaginary spectrum and corresponding dense and minimal family of eigenvectors, which however does not form a Schauder basis. We obtain two-sided estimates for norms of C0-groups from this class and thus prove that these C0-groups have linear growth. Moreover we show that C0-groups from the considered class do not have any maximal asymptotics. This means that the fastest growing orbits do not exist.

Mathematics Subject Classification 2010: 47D06, 34G10, 46B45, 34K25
Key words: C0-group, linear growth, maximal asymptotics, XYZ theorem

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