Lyapunov theorems for Banach spaces
classification
🧮 math.FA
math.SP
keywords
banachcharacterizationdichotomydifferentialequationsevolutionaryexponentialfunctions
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We present a spectral mapping theorem for semigroups on any Banach space $E$. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for $E$-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.
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