  Let $V\subset\R^m$ be a centrally symmetric convex body and let
$V^*\subset\R^m$ be its polar. We prove limit relations between the sharp
constants in the multivariate Markov-Bernstein-Nikolskii type inequalities for
algebraic polynomials on $V^*$ and the corresponding constants for entire
functions of exponential type with the spectrum in $V$.
