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Uniformly continuous superposition operators in the space of functions of bounded n-dimensional Pdbl -variation

Abstract:

We prove that if a superposition operator maps a subset of the space of all metric-vector-space-valued-functions of bounded n-dimensional Pdbl -variation into another such space, and is uniformly continuous, then the generating function of the operator is an affine function in the functional variable. © Copyright by Faculty of Mathematics and Information Science, Warsaw University of Technology.