On doubly stochastic quadratic operators and Birkhoff's problem
Rasul Ganikhodzhaev, Farruh Shahidi · arXiv (Cornell University) · 2008
In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms convex polytope. Finally, we study analogue of Birkhoff's theorem for the class of doubly stochastic quadratic operators.