Generalized Markov–Bernstein Inequalities and Stability of Dynamical Systems

We analyze the Markov–Bernstein type inequalities between norms of functions and their derivatives for complex exponential polynomials. establish a relation sharp constants in these stability problem linear switching systems. In particular, maximal discretization step is estimated. prove monotonicity with respect to exponents, provided those exponents are real. This gives asymptotically tight uniform bounds general form extremal polynomial. The case exponent left as an open problem.