On doubly stochastic quadratic operators and Birkhoff's problem

Details On doubly stochastic quadratic operators and Birkhoff's problem On doubly stochastic quadratic operators and Birkhoff's problem

2008-02-08

arxiv.org/abs/0802.1100v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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.

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