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arXiv · 0802.1100

On doubly stochastic quadratic operators and Birkhoff's problem

Rasul Ganikhodzhaev·Farruh Shahidi
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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.

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Rasul Ganikhodzhaev, Farruh Shahidi. 2008-02-08. On doubly stochastic quadratic operators and Birkhoff's problem. https://arxiv.org/abs/0802.1100

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