A Remez-Type Inequality for Non-dense Müntz Spaces with Explicit Bound Academic Article uri icon

abstract

  • Let Λ := (λk)∞k=0 be a sequence of distinct nonnegative real numbers with λ0 := 0 and ∑∞k=1 1/λk < ∞. Let ρ ∈ (0, 1) and ε ∈ (0, 1 - ρ) be fixed. An earlier work of the authors shows that C(Λ, ε, ρ) := sup{∥p∥ [0, ρ] : p ∈ span{xλ0, xλ1, ...}, m({x∈[ρ, 1] : |p(x)|≤1}) ≥ ε} is finite. In this paper an explicit upper bound for C(Λ, ε, ρ) is given. In the special case λk := kα, α > 1, our bounds are essentially sharp. © 1998 Academic Press.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 1

publication date

  • June 1998