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Abstract

Conditions under which the inf-convolution of f and g $f □ g(x):= inf_{y+z=x}(f(y)+g(z))$ has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions $f: X → ℝ ∪ {+∞}$ on a reflexive Banach space such that $ lim_{∥x∥ → ∞} f(x)/∥x∥ = ∞$ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.