Asymptotic Behavior of Nikolskii Constants for Polynomials on the Unit Circle
نویسندگان
چکیده
Let q > p > 0, and consider the Nikolskii constants Λn,p,q = inf deg(P )≤n−1 ‖P‖p ‖P‖q , where the norm is with respect to normalized Lebesgue measure on the unit circle. We prove that lim sup n→∞ n 1 p − 1 q Λp,q ≤ Ep,q , where Ep,q = inf ‖f‖Lp(R) ‖f‖Lq(R) , and the inf is taken over all entire functions f of exponential type at most π. We conjecture that the lim sup can be replaced by a limit. Nikolskii Inequalities, Paley-Wiener Spaces 42C05
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