On vector-valued curves that allow a C
1,α parametrization |
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| Authors: | J Duda L Zajíček |
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| Institution: | 1. PIRA Energy Group, 3 Park Avenue, 26th Floor, New York, NY, 10016, USA
2. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8-Karlín, Czech Republic
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| Abstract: | Let X be a Banach space and α ∈ (0, 1]. We find equivalent conditions for a function f: 0,1] → X to admit an equivalent parametrization, which is C 1,α (i.e., has α-Hölder derivative). For X = ?, a characterization is well-known. However, even in the case X = ?2 several new ideas are needed. |
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