Geodesic
Linear Functional-Differential Equations in a Banach Algebra*
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 435-439

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The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting. The method, based on functional analysis, had been used extensively by L. Cesari [1] in similar forms for boundary value problems, and by J. K. Hale, S. Bancroft, and D. Sweet [2]. We also obtain as corollaries several results for ordinary differential equations in Banach algebras which were proved in a different way by Hille. 
Fitzpatrick, W. J.; Grimm, L. J. Linear Functional-Differential Equations in a Banach Algebra*. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 435-439. doi: 10.4153/CMB-1978-076-3
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     author = {Fitzpatrick, W. J. and Grimm, L. J.},
     title = {Linear {Functional-Differential} {Equations} in a {Banach} {Algebra*}},
     journal = {Canadian mathematical bulletin},
     pages = {435--439},
     year = {1978},
     volume = {21},
     number = {4},
     doi = {10.4153/CMB-1978-076-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-076-3/}
}
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