Newman's Inequality for Müntz Polynomials on Positive Intervals

Newman’s Inequality for Müntz Polynomials on Positive Intervals

The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem (Newman’s Inequality on [a, b] ⊂ (0,∞)). Let Λ := (λj)j=0 be an increasing sequence of nonnegative real numbers. Suppose λ0 = 0 and there exists a δ > 0 so that λj ≥ δj for each j. Suppose 0 < a < b. Then there exists a constant c(a, b, δ) depending only on a, b, and δ so that ‖P ′‖[a,b] ≤ ...

Müntz Systems and Orthogonal Müntz - Legendre Polynomials

The Müntz-Legendre polynomials arise by orthogonalizing the Müntz system {xxo, xx¡, ...} with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Müntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Lague...

The Full Markov-newman Inequality for Müntz Polynomials on Positive Intervals

For a function f defined on an interval [a, b] let ‖f‖[a,b] := sup{|f(x)| : x ∈ [a, b]} . The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let n ≥ 1 be an integer. Let λ0, λ1, . . . , λn be n + 1 distinct real numbers. Let 0 < a < b. Then

The Cauchy-Schwarz Inequality and Positive Polynomials

Markov-Type Inequalities for Products of Müntz Polynomials

Let Λ := (λj) ∞ j=0 be a sequence of distinct real numbers. The span of {xλ0 , x1 , . . . , xλn} over R is denoted by Mn(Λ) := span{xλ0 , x1 , . . . , xλn}. Elements of Mn(Λ) 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 Λ := (λj) ∞ j=0 and Γ := (γj) ∞ j=0 be increasing sequences of no...