论文标题
马尔可夫·伯恩斯坦（Markov-Bernstein）的普遍不平等和动力学系统的稳定性
Generalized Markov-Bernstein inequalities and stability of dynamical systems
论文作者
论文摘要
分析功能范围及其衍生物之间的马尔可夫 - 伯恩斯坦类型不平等，以分析复杂的指数多项式。我们在这些不平等现象中建立了尖锐常数与线性切换系统的稳定性问题之间的关系。特别是，估计了最大离散步骤。如果这些指数是真实的，我们证明了尖锐常数相对于指数的单调性。这给出了渐近均匀的统一边界和极端多项式的一般形式。复杂指数的情况是一个开放问题。
The Markov-Bernstein type inequalities between the norms of functions and of their derivatives are analysed for complex exponential polynomials. We establish a relation between the sharp constants in those inequalities and the stability problem for linear switching systems. In particular, the maximal discretization step is estimated. We prove the monotonicity of the sharp constants with respect to the exponents, provided those exponents are real. This gives asymptotically tight uniform bounds and the general form of the extremal polynomial. The case of complex exponent is left as an open problem.
