The direct and inverse theorems of the approximation theory for solutions of differential equations in a Banach space - Gorbachuk, M. L.; Gorbachuk, V. M. (Reports of the National Academy of Sciences of Ukraine, 2016)
An equation of the form y ′ (t) = Ay(t), t ∈ (−∞,∞), where A is the generator of a C0-group of linear operators on a Banach space, is considered. The direct and inverse theorems of the theory of approximation of weak solutions of this equation by entire solutions of exponential type, which establish the one-to-one correspondence between the order of convergence to zero of the best approximation of a solution and its smoothness degree, are presented.