V. A. Markov's theorems in normed spaces

摘要

We obtain multidimensional analogues of V. A. Markov's inequalities for algebraic polynomials on centrally symmetric convex bodies and an analogue of the Schaeffer-Duffin inequality for polynomials on multidimensional cubes. We establish necessary and sufficient conditions for these inequalities to become equalities, and describe the sets of extremals.