caa a22 4500 46793228X CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s00020-004-1351-3 doi (NATIONALLICENCE)springer-10.1007/s00020-004-1351-3 Riedle Markus Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, D-10099, Berlin, Germany aut Lyapunov Exponents for Linear Delay Equations in Arbitrary Phase Spaces [Elektronische Daten] [Markus Riedle] Abstract.: A linear integral equation with infinite delay is considered where the admissible function space $$\mathcal{B}$$ of initial conditions is as usually only described axiomatically. Merely using this axiomatic description, the long time behavior of the solutions is determined by calculating the Lyapunov exponents. The calculation is based on a representation of the solution in the second dual space of $$\mathcal{B}$$ and on a connection between the asymptotic behavior of the solutions of the integral equation under consideration and its adjoint equation subject to the spectral decomposition of the space of initial functions. We apply the result to an example of a stochastic differential equation with infinite delay. Birkhäuser Verlag, Basel, 2006 Lyapunov exponents nationallicence differential equations with infinite delay nationallicence weak*-integral nationallicence abstract phase space nationallicence variation of constants formula nationallicence stochastic differential equations with delay nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/2(2006-02-01), 259-278 0378-620X 54:2<259 2006 54 20 https://doi.org/10.1007/s00020-004-1351-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1351-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Riedle Markus Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, D-10099, Berlin, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/2(2006-02-01), 259-278 0378-620X 54:2<259 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer