论文标题
GGR猜想的概括
A Generalization of the GGR Conjecture
论文作者
论文摘要
对于每个正整数$ n $，功能$ f $和点$ c $，ggr定理指出，$ f $是$ n $ times peano peano在$ c $时在$ c $时以$ c $ in $ c $而且仅当$ f $ as $ f $ as $ n-1 $ times peano在$ c $ c $ c $ c $ and $ n $ and $ n $ th $ n $ f $ f $ f $ c $ c $ co $ prel prel a im_ fre fre freac} 1{h^{n}}\sum_{i=0}^n(-1)^i\binom{n}{i}f(c+(n-i-k)h), \] for $k=0,\ldots,n-1$.该定理最近在[AC2]中得到了证明，并且自1998年以来一直是Ghinchev，Guerragio和Rocca的猜想。我们提供了该定理的新证明，基于其概括，它产生了$ N $ n $ th $ th $ th $ th $ th riemann平滑度条件，这些条件可以在GGR定理中发挥上述作用。
For each positive integer $n$, function $f$, and point $c$, the GGR Theorem states that $f$ is $n$ times Peano differentiable at $c$ if and only if $f$ is $n-1$ times Peano differentiable at $c$ and the following $n$-th generalized Riemann~derivatives of $f$ at $c$ exist: \[ \lim_{h\rightarrow 0}\frac 1{h^{n}}\sum_{i=0}^n(-1)^i\binom{n}{i}f(c+(n-i-k)h), \] for $k=0,\ldots,n-1$. The theorem has been recently proved in [AC2] and has been a conjecture by Ghinchev, Guerragio, and Rocca since 1998. We provide a new proof of this theorem, based on a generalization of it that produces numerous new sets of $n$-th Riemann smoothness conditions that can play the role of the above set in the GGR Theorem.
