AN EXTREMAL PROBLEM CONCERNING A MARKOV-TYPE INEQUALITY

For any polynomial f with complex coefficients let parallel-to f parallel-to be the norm in L2[0, infinity) with the Laguerre weight function w(t) = e(-t). Let P(n) be the set of all complex polynomials whose degree does not exceed n and gamma-n := sup f member-of P(n) (parallel-to f' parallel-to/parallel-to f parallel). We show that gamma-n/n --> 2/pi as n --> infinity.