Newman's inequality for Muntz polynomials on positive intervals Academic Article uri icon

abstract

  • The principal result of this paper is the following Markov-type inequality for Mntz polynomials. THEOREM (Newman's Inequality on [a, b] (0, )). Let A := (j)j=0be an increasing sequence of nonnegative real numbers. Suppose 0 = 0 and there exists a > 0 so that j j for each j. Suppose 0 < a < b. Then there exists a constant c(a, b, ) depending only on a, b, and so that (equation presented) for every P Mn(), where Mn() denotes the linear span of {x 0, x1, ..., xn} over . When [a, b] = [0, 1] and with P[a, b] replaced with xP(x)[a, b] this was proved by Newman. Note that the interval [0, 1] plays a special role in the study of Mntz spaces Mn(). A linear transformation y = x + does not preserve membership in Mn() in general (unless = 0). So the analogue of Newman's Inequality on [a, b] for a > 0 does not seem to be obtainable in any straightforward fashion from the [0, b] case. 1996 Academic Press, Inc.

published proceedings

  • JOURNAL OF APPROXIMATION THEORY

author list (cited authors)

  • Borwein, P., & Erdelyi, T.

citation count

  • 4

complete list of authors

  • Borwein, Peter||Erdélyi, Tamás

publication date

  • May 1996