Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone
Volume 179 / 2007
Studia Mathematica 179 (2007), 263-275 MSC: 39B52, 39B22, 17A15, 62H05. DOI: 10.4064/sm179-3-4
It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.