English

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.

Keywords

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

R2 v1 2026-06-21T10:10:44.313Z