双随机二次算子与Birkhoff问题
On doubly stochastic quadratic operators and Birkhoff's problem
摘要：
本文引入了双随机二次算子的概念。证明了算子双随机性的充要条件。此外，我们还证明了所有双随机算子的集合构成凸多胞体。最后，我们研究了双随机二次算子类的Birkhoff定理的模拟。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
