Uniformly continuous superposition operators in the space of bounded variation functions |
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| Authors: | Janusz Matkowski |
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| Affiliation: | 1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Podgórna 50, PL‐65246 Zielona Góra, Poland;2. Institute of Mathematics, Silesian University, Bankowa 14, PL‐40007 Katowice, Poland |
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| Abstract: | ![]()
Let I, J ? ? be intervals. The main result says that if a superposition operator H generated by a function of two variables h: I × J → ?, H (φ)(x) ? h (x, φ (x)), maps the set BV (I, J) of all bounded variation functions, φ: I → J into the Banach space BV (I, ?) and is uniformly continuous with respect to the BV ‐norm, then h (x, y) = a (x)y + b (x), x ∈ I, y ∈ J, for some a, b ∈ BV (I, ?) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Superposition operator Lipschitzian operator uniformly continuous operator bounded variation function |
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