The cancellation law for inf-convolution of convex functions

Tom 110 / 1994

Dariusz Zagrodny Studia Mathematica 110 (1994), 271-282 DOI: 10.4064/sm-110-3-271-282


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.


  • Dariusz Zagrodny

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