Curves in Banach spaces which allow a C2-parameterization

被引：1

作者：

Duda, Jakub ^{[1
]}

Zajicek, Ludek ^{[2
]}

机构：

[1] PIRA Energy Grp, New York, NY 10016 USA

[2] Charles Univ Prague, Fac Math & Phys, Prague 18675 8, Karlin, Czech Republic

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2011年 / 83卷

关键词：

ALPHA-VARIATION; DIFFERENTIABILITY;

D O I：

10.1112/jlms/jdq100

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a complete characterization of those f : [0, 1] --> X (where X is a Banach space that has a Frechet smooth norm) that allow an equivalent C-2 - parameterization. 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 parameterizations with a bounded second derivative is solved.

引用

页码：733 / 754

页数：22

共 17 条

[1] Benyamini Y., 2000, Colloquium Publications, V48
[2] Bruckner A., 1994, CRM Monograph Series, V5
[3] Chistyakov V. V., 1997, J. Dyn. Control Syst., V3, P261, DOI [10.1007/BF02465896, DOI 10.1007/BF02465896]
[4] On positively differentiable curves with values in normed linear spaces
Duda, J
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (02) : 662 - 674
[5] On vector-valued curves that allow a C 1,α parametrization
Duda, J.
Zajicek, L.
[J]. ACTA MATHEMATICA HUNGARICA, 2010, 127 (1-2) : 85 - 111
[6] DUDA J, 2006, ARXIVMATH0603735V1
[7] Second order differentiability of paths via a generalized 1/2-variation
Duda, Jakub
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (01) : 628 - 638
[8] Curves in Banach spaces-differentiability via homeomorphisms
Duda, Jakub
Zajicek, Ludek
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2007, 37 (05) : 1493 - 1525
[9] Generalized α-variation and Lebesgue equivalence to differentiable functions
Duda, Jakub
[J]. FUNDAMENTA MATHEMATICAE, 2009, 205 (03) : 191 - 217
[10] Federer Herbert, 1969, GEOMETRIC MEASURE TH

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