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We study linear cocycles generated by nonautonomous delay equations in aproper Hilbert space and their extensions (compound cocycles) to exteriorpowers. Armed with the recently developed version of the Frequency Theorem, wedevelop analytic perturbation techniques for comparison of spectral propertiesbetween such cocycles and cocycles generated by stationary equations. Inparticular, the developed machinery is applied for studying uniform exponentialdichotomies and obtaining effective dimension estimates for invariant setsarising in nonlinear problems. Our conditions are given by strict frequencyinequalities involving resolvents of additive compound operators associatedwith stationary problems. Computing such operators requires solving afirst-order PDEs with boundary conditions containing both partial derivativesand delays. However, to test frequency inequalities, the problem reduces tocomputation of norms of certain operators that can be done numerically andreflects computational complexity of the problem.

Spectral comparison of compound cocycles generated by delay equations in Hilbert spaces