On the Roughness of Quasinilpotency Property of One-parameter Semigroups
Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 364-371
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Let $\mathbf{S}:={{\{S(t)\}}_{t\ge 0}}$ be a ${{\text{C}}_{0}}$ -semigroup of quasinilpotent operators (i.e., $\sigma (S(t))=\{0\}$ for each $t>0$ ). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical finite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a ${{\text{C}}_{0}}$ -semigroup is preserved under the perturbations of its infinitesimal generator.
Mots-clés :
34D05, 34D10, 34E10, one-parameter semigroups, quasinilpotency, superstability, essential spectrum.
Preda, Ciprian. On the Roughness of Quasinilpotency Property of One-parameter Semigroups. Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 364-371. doi: 10.4153/CMB-2016-088-0
@article{10_4153_CMB_2016_088_0,
author = {Preda, Ciprian},
title = {On the {Roughness} of {Quasinilpotency} {Property} of {One-parameter} {Semigroups}},
journal = {Canadian mathematical bulletin},
pages = {364--371},
year = {2017},
volume = {60},
number = {2},
doi = {10.4153/CMB-2016-088-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-088-0/}
}
TY - JOUR AU - Preda, Ciprian TI - On the Roughness of Quasinilpotency Property of One-parameter Semigroups JO - Canadian mathematical bulletin PY - 2017 SP - 364 EP - 371 VL - 60 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-088-0/ DO - 10.4153/CMB-2016-088-0 ID - 10_4153_CMB_2016_088_0 ER -
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