Closed semistable operators and singular differential equations

Jaromír J. Koliha; Trung Dinh Tran

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 605-620
  • ISSN: 0011-4642

Abstract

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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which 0 is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of C 0 -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.

How to cite

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Koliha, Jaromír J., and Tran, Trung Dinh. "Closed semistable operators and singular differential equations." Czechoslovak Mathematical Journal 53.3 (2003): 605-620. <http://eudml.org/doc/30802>.

@article{Koliha2003,
abstract = {We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.},
author = {Koliha, Jaromír J., Tran, Trung Dinh},
journal = {Czechoslovak Mathematical Journal},
keywords = {closed linear operator; $C_0$-semigroup; infinitesimal generator; semistable operator; singular differential equation; closed linear operator; -semigroup; infinitesimal generator; singular differential equation},
language = {eng},
number = {3},
pages = {605-620},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Closed semistable operators and singular differential equations},
url = {http://eudml.org/doc/30802},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Koliha, Jaromír J.
AU - Tran, Trung Dinh
TI - Closed semistable operators and singular differential equations
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 605
EP - 620
AB - We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.
LA - eng
KW - closed linear operator; $C_0$-semigroup; infinitesimal generator; semistable operator; singular differential equation; closed linear operator; -semigroup; infinitesimal generator; singular differential equation
UR - http://eudml.org/doc/30802
ER -

References

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