Second order differentiability of paths via a generalized 1/2-variation
| dc.creator | Duda, Jakub | |
| dc.date | 2005-11-21 | |
| dc.date | 2006-07-16 | |
| dc.date.accessioned | 2026-07-07T06:51:32Z | |
| dc.date.available | 2026-07-07T06:51:32Z | |
| dc.description | We find an equivalent condition for a continuous vector-valued path to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a $VBG_{1/2}$ function, which plays an analogous role for the second order differentiability as the classical notion of a $VBG_*$ function for the first order differentiability. In fact, for a function $f:[a,b]\to X$, being Lebesgue equivalent to a twice differentiable function is the same as being Lebesgue equivalent to a differentiable function with a pointwise Lipschitz derivative. We also consider the case when the first derivative can be taken non-zero almost everywhere. | |
| dc.description | generalized version; new title; 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511518 | |
| dc.identifier | http://arxiv.org/abs/math/0511518 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105017 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 14H50; 53A04 | |
| dc.title | Second order differentiability of paths via a generalized 1/2-variation | |
| dc.type | text |