Abstract
It is the purpose of these notes to describe the theory of Hale and Kato for functional differential equations based on a space of initial data which satisfy some very reasonable axioms. We also indicate some recent results of Naito showing how extensive the theory of linear systems can be developed in an abstract setting in particular, the characterization of the spectrum of the infinitesimal generator together with the decomposition theory and exponential estimates of solutions.
This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3092A, in part by the National Science Foundation under NSF-MCS 78-18858, and in part by the United States Army under ARO-D-31-124-73-G130.
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Hale, J.K. (1979). Retarded equations with infinite delays. In: Peitgen, HO., Walther, HO. (eds) Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064317
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DOI: https://doi.org/10.1007/BFb0064317
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