Sharp polynomial bounds for certain C0-groups generated by operators with non-basis family of eigenvectors

被引：2

作者：

Sklyar, Grigory M. ^{[1
,3
]}

Marchenko, Vitalii ^{[2
]}

Polak, Piotr ^{[1
]}

机构：

[1] Univ Szczecin, Inst Math, Wielkopolska 15, PL-70451 Szczecin, Poland

[2] Natl Acad Sci Ukraine, B Verkin Inst Low Temp Phys & Engn, Math Div, Prospekt Nauky 47, UA-61103 Kharkiv, Ukraine

[3] Kharkov Natl Univ, Svobody Sq 4, UA-61022 Kharkiv, Ukraine

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2021年 / 280卷 / 07期

关键词：

C-0-group; Polynomially bounded semigroup; Maximal asymptotics; XYZ theorem;

D O I：

10.1016/j.jfa.2020.108864

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sharp polynomial bounds for norms of C-0-groups generated by operators with purely imaginary eigenvalues lambda(n) = i ln n, n is an element of N, and complete minimal non-basis family of eigenvectors, constructed recently by G. Sklyar and V. Marchenko in [17], are obtained. Besides, it is shown that these C-0-groups do not have a maximal asymptotics. For the more general case of behaviour of the spectrum of operators we present the proof of one lemma concerning the behaviour of j-th differences of sequences of complex exponentials exp(it f(n)), n is an element of N, that is used in [17] to obtain bounds from above for norms of corresponding C-0-groups. Also the growth properties of the resolvent for generators of constructed C-0-groups are discussed. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：29