On the denseness of span{xλj(1−x)1−λj} in C0([0,1]) Academic Article uri icon

abstract

  • Associated with a sequence Λ = (λj)j = 0∞ of distinct exponents λj ∈ [0, 1], we defineH (Λ) : = span {xλ0 (1 - x)1 - λ0, xλ1 (1 - x)1 - λ1, ...} ⊂ C ([0, 1]) . Answering a question of Giuseppe Mastroianni, we show that H (Λ) is dense inC0 [0, 1] : = {f ∈ C [0, 1] : f (0) = f (1) = 0} in the uniform norm on [0, 1] if and only ifunderover(∑, j = 0, ∞) (1 / 2 - | 1 / 2 - λj |) = ∞ . © 2006 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Erdélyi, T.

citation count

  • 0

publication date

  • September 2006