Equivalences between nonuniform exponential dichotomy and admissibility (Q338469)

This paper is dedicated to the study of the relationship between exponential dichotomies and admissibility of function classes for linear systems of differential equations NEWLINE\[NEWLINEx'= A(t)x\quad (x\in\mathbb R^n).NEWLINE\]NEWLINE It is proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs are found to imply a nonuniform exponential dichotomy.NEWLINENEWLINEThe main results are contained in Theorem 1 (nonuniform exponential dichotomy on half-lines \(\mathbb R_\pm\) separately), Theorem 2 (nonuniform exponential dichotomy on both half-lines \(\mathbb R_\pm\) simultaneously) and Theorem 3 (nonuniform exponential dichotomy on the whole line \(\mathbb R\)).