Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone

作者：Wesolowski Jacek^*

来源：Studia Mathematica, 2007, 179(3): 263-275.

DOI：10.4064/sm179-3-4

• Cauchy equation
• equation of ratios
• Lorentz cone
• determinant
• generalized power function
• Lukacs characterization

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.

• 出版日期2007