Orthogonality preserving infinite dimensional quadratic stochastic operators - Akin, Hasan; Mukhamedov, Farrukh (American Institute of Physics, 2015)
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.