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Characterizations of dichotomies of evolution equations on the half-line. (English) Zbl 0995.34038
The authors characterize (ordinary and exponential) dichotomies of an evolution family $U(t,s)$, $t \geq s$, of bounded linear operators on a Banach space $X$ in terms of properties of certain operators $I_0$ and $I_X$ which are defined on subspaces of $L_p(\bbfR_+,X)$ using the integral equation $$ u(t) = U(t,s) u(s) + \int_s^t U(t,\xi) f(\xi) d\xi .$$

34D09Dichotomy, trichotomy
34G10Linear ODE in abstract spaces
47D03(Semi)groups of linear operators
Full Text: DOI
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