The chain rule for F-differentiation
Chaobankoh, T. and Feinstein, Joel and Morley, S. (2016) The chain rule for F-differentiation. Irish Mathematical Society Bulletin (77). pp. 19-34. ISSN 0791-5578
Official URL: http://www.maths.tcd.ie/pub/ims/bull77/Feinstein.pdf
Let X be a perfect, compact subset of the complex plane, and let D (1)(X) denote the (complex) algebra of continuously complex-differentiable functions on X. Then D(1)(X) is a normed algebra of functions but, in some cases, fails to be a Banach function algebra. Bland and the second author investigated the completion of the algebra D(1)(X), for certain sets X and collections F of paths in X, by considering F-differentiable functions on X.
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