Homogeneous Functions and Conjugacy

(Positively) homogeneous functions play a special role in the Legendre-Fenchel duality. The Legendre-Fenchel conjugate of a p-homogeneous function is a q-homogeneous function with 1/p+1/q= 1. Further properties of the function, its conjugate, and of the maximizers are also derived. The same result also holds in the Max-Prod and Min-Max algebra for the analogue of the Legendre-Fenchel transform.