Title:
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Curves in Banach spaces which allow a $C^{1,\rm BV}$ parametrization or a parametrization with finite convexity (English) |
Author:
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Duda, Jakub |
Author:
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Zajíček, Luděk |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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63 |
Issue:
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4 |
Year:
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2013 |
Pages:
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1057-1085 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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 $X = \mathbb R^2$. (English) |
Keyword:
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curve in Banach spaces |
Keyword:
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$C^{1,\rm BV}$ parametrization |
Keyword:
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parametrization with bounded convexity |
MSC:
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26A51 |
MSC:
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26E20 |
MSC:
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53A04 |
idZBL:
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Zbl 06373962 |
idMR:
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MR3165515 |
DOI:
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10.1007/s10587-013-0072-7 |
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Date available:
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2014-01-28T14:18:13Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/143617 |
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Reference:
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