Local operators and a characterization of the Volterra operator - Matkowski, Janusz (Annals of functional analysis, 2010)
We consider locally defined operators of the form [D.sub.n] o K where D is the operator of differentiation and K maps the space of continuous functions into the space of n-times differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed. 2010 Mathematics Subject Classification. Primary 47H30; Secondary 47A67. Key words and phrases. Nemytskij operator, locally defined operator, superposition operator, Volterra operator, differentiable functions, analytic functions.