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Journal of Mathematical Sciences

, Volume 139, Issue 6, pp 7151–7164 | Cite as

Completeness of orthogonal systems in asymmetric spaces with sign-sensitive weight

  • A. I. Kozko
Article
  • 13 Downloads

Abstract

We study the problem on the completeness of orthogonal systems in asymmetric spaces with sign-sensitive weight. Theorems of general form are obtained. In particular, the necessary and sufficient conditions on α, β, q 1, and q 2 for which the known orthogonal systems are everywhere dense in asymmetric spaces L (α,β);q ([0, 1]) are found.

Theorem. Let α, β, q 1, q 2 ∈ [1,+∞]. The following orthogonal systems are dense in asymmetric spaces L (α,β);q ([0, 1]) if and only if either max{α, β, q 1, q 2} < + ∞ or max {α, β} < +∞, q 1 = q 2 = +∞: trigonometric, algebraic, Haar’s system, Meyer’s system of wavelets, Shannon-Kotel’nikov wavelets, Stromberg and Lemarie-Battle wavelets, the Walsh system, and the Franklin system.

Keywords

Closed Interval Trigonometric Polynomial Orthogonal System Linear Hull Weierstrass Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. I. Kozko
    • 1
  1. 1.Moscow State UniversityMoscow

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