Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time

V. Khatskevich, and L. Zelenko. "Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time." Studia Mathematica 177.3 (2006): 195-210. <http://eudml.org/doc/285200>.

@article{V2006,
abstract = {We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature of the indefinite metric.},
author = {V. Khatskevich, L. Zelenko},
journal = {Studia Mathematica},
keywords = {linear difference equation in Hilbert space; plus-operator; linear fractional relation; dichotomous behavior},
language = {eng},
number = {3},
pages = {195-210},
title = {Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time},
url = {http://eudml.org/doc/285200},
volume = {177},
year = {2006},
}

TY - JOUR
AU - V. Khatskevich
AU - L. Zelenko
TI - Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
JO - Studia Mathematica
PY - 2006
VL - 177
IS - 3
SP - 195
EP - 210
AB - We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature of the indefinite metric.
LA - eng
KW - linear difference equation in Hilbert space; plus-operator; linear fractional relation; dichotomous behavior
UR - http://eudml.org/doc/285200
ER -