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Sibirsk. Mat. Zh., 2010, Volume 51, Number 2, Pages 410–419 (Mi smj2094)  

This article is cited in 2 scientific papers (total in 2 papers)

Obstructions to the uniform stability of a $C_0$-semigroup

K. V. Storozhuk

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Let $T_t\colon X\to X$ be a $C_0$-semigroup with generator $A$. We prove that if the abscissa of uniform boundedness of the resolvent $s_0(A)$ is greater than zero then for each nondecreasing function $h(s)\colon\mathbb R_+\to\mathbb R_+$ there are $x'\in X'$ and $x\in X$ satisfying $\int_0^\infty h(|\langle x',T_tx\rangle|) dt=\infty$. If $i\mathbb R\cap\operatorname{Sp}(A)\ne\varnothing$ then such $x$ may be taken in $D(A^\infty)$.

Keywords: exponentially stable operator semigroup.

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English version:
Siberian Mathematical Journal, 2010, 51:2, 330–337

Bibliographic databases:

UDC: 517.986.7
Received: 16.02.2009

Citation: K. V. Storozhuk, “Obstructions to the uniform stability of a $C_0$-semigroup”, Sibirsk. Mat. Zh., 51:2 (2010), 410–419; Siberian Math. J., 51:2 (2010), 330–337

Citation in format AMSBIB
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\by K.~V.~Storozhuk
\paper Obstructions to the uniform stability of a~$C_0$-semigroup
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 2
\pages 410--419
\mathnet{http://mi.mathnet.ru/smj2094}
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\transl
\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 2
\pages 330--337
\crossref{https://doi.org/10.1007/s11202-010-0034-3}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952040150}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Buse C., Khan A., Rahmat G., Saierli O., “Weak Real Integral Characterizations For Exponential Stability of Semigroups in Reflexive Spaces”, Semigr. Forum, 88:1 (2014), 195–204  crossref  mathscinet  zmath  isi  elib  scopus
    2. Glueck J., “on Weak Decay Rates and Uniform Stability of Bounded Linear Operators”, Arch. Math., 104:4 (2015), 347–356  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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