Sharp Constants of Approximation Theory. I. Multivariate Bernstein-Nikolskii Type Inequalities

摘要

Given a centrally symmetric convex body V subset of Rm, let TaV be the set of all trigonometric polynomials with the spectrum in aV,a>0, and let BV be the set of all entire functions of exponential type with the spectrum in V. We discuss limit relations between the sharp constants in the multivariate Bernstein-Nikolskii inequalities defined by infinity Pp,q,DN,a,V,Ep,infinity,DN,V=lim(a ->infinity) P-p,P-infinity,DN,a,V.