A REMEZ-TYPE INEQUALITY FOR NONDENSE MUNTZ-SPACES WITH EXPLICIT BOUND

Let Lambda := (lambda(k))(k=0)(infinity) be a sequence of distinct non negative real numbers with lambda(0) := 0 and Sigma(k=1)(infinity) 1/l ambda(k) < infinity. Let rho is an element of (0, 1) and epsilon is an element of (0, 1 - rho) be fixed. An earlier work of the authors show s that C(Lambda, epsilon, rho) := sup{ \\p\\([0, rho]) : p is an eleme nt of span {x(lambda 0), x(lambda 1), ...}, m({x epsilon [rho, 1] : \p (x)\ less than or equal to 1}) greater than or equal to epsilon} is fi nite. In this paper an explicit upper bound for C(Lambda, epsilon, rho ) is given. In the special case lambda(k) := k(alpha), alpha > 1, our bounds are essentially sharp. (C) 1998 Academic Press.