Curves in Banach Spaces Which Allow a C Parametrization or a Parametrization with Finite Convexity
نویسنده
چکیده
We give a complete characterization of those f : [0, 1]→ X (where X is a Banach space) which allow an equivalent (smooth) parametrization with finite convexity, and (in the case when X has a Fréchet smooth norm) a C parametrization. For X = R, a characterization for the C case is well-known. However, even in the case X = R, several quite new ideas are needed.
منابع مشابه
Curves in Banach spaces which allow a C2-parameterization
We give a complete characterization of those f : [0, 1] → X (where X is a Banach space which admits an equivalent Fréchet smooth norm) which allow an equivalent C 2 parametrization. For X = R, a characterization is well-known. However, even in the case X = R 2 , several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved.
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