Applied Analysis Seminar

Tuesday June 25 in K9509, SFU

Speaker and Title: 2:00 - 2:45: Rafal Goebel (CECM/UBC) "Convex integral functionals and Fenchel duality"

Abstract: A survey of the basic properties of conve integral functionals, their conjugates and subgradients will be given.

Speaker and Title: 2:45 - 3:30: Xianfu Wang (Okanagan University College) "Cone monotone functions: differentiability and continuity"

Abstract: Assume that X is a Banach space and K is a convex cone in X with non-empty interior. Let f be a real function on X that is K-monotone. For any two directions u,v in the interior of K, the set of points at which the property

if f'(x,u) and f'(x,v) exist, then f'(x,.) is linear on the span of u,v
holds has a sigma-porous complement. When X is separable, this gives a stronger version of a result of Borwein, Burke and Lewis. We also show that f is universally measurable, and f is continuous everywhere on X except for a sigma-porous set.