关于分离凸函数迹问题的注记
Notes on the trace problem for separately convex functions
摘要：
本文讨论了如下问题：对于一个在坐标轴方向上凸的二元或多元函数f，它的迹g（x）= f（x，x，.，x）看起来像什么？在二维的情况下，我们提供了一些充要条件和充分条件，以及一些例子说明，我们的方法似乎并不适合寻找一个全面的一般性的特征。然而，对于凹函数g，建立了二维情况下的特征。
英文摘要：
We discuss the following question: For a function f of two or more variables which is convex in the directions of coordinate axes, how can its trace g(x) = f(x, x, ..., x) look like? In the two-dimensional case, we provide some necessary and sufficient conditions, as well as some examples illustrating that our approach does not seem to be appropriate for finding a characterization in full generality. For a concave function g, however, a characterization in the two-dimensional case is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
