The paper concerns a biunique correspondence between some positively homogeneous functions on ℝn and some star-shaped sets with nonempty interior, symmetric with respect to the origin (Theorems 3.5 and 4.3).
Authors:Frédéric Magoulès and Guillaume Gbikpi-Benissan
Duchon J. Splines minimizing rotation-invariant semi-norms in Sobolev spaces, in Constructive Theory of Functions of Several Variables , W. Schempp and K. Zeller, (Eds.) Springer, 1977, pp. 85–100.