On doubly stochastic quadratic operators and Birkhoff's problem

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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.
18 pages

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Functional Analysis, Dynamical Systems, 15A51; 15A63; 46T99; 46A55

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http://salesiana.dossiersoluciones.com/handle/123456789/154434

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.1100
 http://arxiv.org/abs/0802.1100

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arXiv