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- W2789084361 abstract "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." @default.
- W2789084361 created "2018-03-06" @default.
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- W2789084361 date "2005-11-21" @default.
- W2789084361 modified "2023-09-27" @default.
- W2789084361 title "Second order differentiability of real functions via a generalized 1/2-variation" @default.
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