Curves in Banach spaces which allow a $C^{1,\rm BV}$ parametrization or a parametrization with finite convexity

Title:

Curves in Banach spaces which allow a $C^{1,\rm BV}$ parametrization or a parametrization with finite convexity

Creator:

Duda, Jakub and Zajíček, Luděk

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:eff4fecf-4d9b-45d8-93d4-2d351de5c13d
uuid:eff4fecf-4d9b-45d8-93d4-2d351de5c13d

Subject:

curve in Banach spaces, $C^{1,\rm BV}$ parametrization, and parametrization with bounded convexity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We give a complete characterization of those $f\colon [0,1] \to X$ (where $X$ is a Banach space) which allow an equivalent $C^{1,\rm BV}$ parametrization (i.e., a $C^1$ parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for $X= \mathbb R^n$. We present examples which show applicability of our characterizations. For example, we show that the $C^{1,\rm BV}$ and $C^2$ parametrization problems are equivalent for $X=\mathbb R$ but are not equivalent for $X = \mathbb R^2$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1057-1085

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:4

Harvested from:

CDK

Metadata only:

false