摘要 : In this paper, we investigate a class of Bernstein functions and a class of completely monotone functions with intriguing applications in convex analysis. We derive representation theorems for Bernstein and completely monotone fun... 展开 In this paper, we investigate a class of Bernstein functions and a class of completely monotone functions with intriguing applications in convex analysis. We derive representation theorems for Bernstein and completely monotone functions with a convexity condition on their measures. These representation theorems are variants of the classical Bernstein and L,vy-Khintchine representation theorems. We show that the transformations that turn a Bernstein function into one having corresponding L,vy measure with harmonically concave tail are the same as the transformations that transform a completely monotone function into one having harmonically convex measure. 收起