Markov-Type Inequalities for Products of Müntz Polynomials Academic Article uri icon

abstract

  • Let ∧: = (λj)∞j=0 be a sequence of distinct real numbers. The span of {xλ0, xλ1, ⋯ , xλn} over ℝ is denoted by Mn(∧):=span{xλ0, xλ1, ⋯ , xλn}. Elements of Mn(λa) are called Müntz polynomials. The principal result of this paper is the following Markov-type inequality for products of Müntz polynomials. Theorem 2.1. Let ∧:=(λj)∞j=0 and Γ :=(γj)∞j=0 be increasing sequences of nonnegative real numbers. Let In particular, 2/3(n+1) λn ≤ K(Mn(∧), Mn(∧)) ≤ 36(2n+1) λn. Under some necessary extra assumptions, an analog of the above Markov-type inequality is extended to the cases when the factor x is dropped, and when the interval [0, 1] is replaced by [a, b] ⊂ (0, ∞). © 2001 Academic Press.

author list (cited authors)

  • Erdélyi, T.

citation count

  • 3

publication date

  • October 2001