On doubly stochastic quadratic operators and Birkhoff's problem
Functional Analysis
2008-02-11 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0802.1100,
title = {On doubly stochastic quadratic operators and Birkhoff's problem},
author = {Rasul Ganikhodzhaev and Farruh Shahidi},
journal= {arXiv preprint arXiv:0802.1100},
year = {2008}
}
Comments
18 pages