Publications [#287219] of Richard Hain

Papers Published

1. Hain, RM, A characterization of smooth functions defined on a Banach space, Proceedings of the American Mathematical Society, vol. 77 no. 1 (October, 1979), pp. 63-67, American Mathematical Society (AMS), ISSN 0002-9939 [2042717], [doi]
   (last updated on 2025/04/05)

   Abstract:
   

   A sufficient condition for a function defined on a Banach space to be ?? C k {C^k} is given. This enables us to characterize the ?? C ∞ {C^\infty } functions from one Banach space into another Banach space as those functions that, for each positive integer m, have the property that the composition of the function with each ?? C ∞ {C^\infty } function from ?? R m {{\mathbf {R}}^m} into the domain of the function is ?? C ∞ {C^\infty } .