Spherically symmetric functions with a convex second derivative and applications to extremal probabilistic problems
We describe the class of all functions φ: [0, ∞)→ℝ for which the second derivative gφDdagger;(x; y, y) of the spherically symmetric function gφ(x):= φ(|x|) in the direction of y is convex in x, where x and y are vectors in a Hilbert space H and |·| is the norm in H. Applications to extremal probabilistic problems are given.
Mathematical Inequalities and Applications
Spherically symmetric functions with a convex second derivative and applications to extremal probabilistic problems.
Mathematical Inequalities and Applications,
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