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Science in China Series A: Mathematics

, Volume 43, Issue 10, pp 1075–1082 | Cite as

Riesz basis, Paley-Wiener class and tempered splines

  • Gensun Fang
  • Jingfan Long
Article

Abstract

The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ℒ2m (T, ℝ) ∩ L2 (ℝ) which is the space of polynomial splines with irregularly distributed nodesT = {t j } j ∈ℤ, where {t j }j∈ℤ is a real sequence such that {e it ξ} j }j ∈ℤ constitutes a Riesz basis for L2([ −π,π]). From these results, the asymptotic relation
is proved, where B π,2 denotes the set of all functions from L2( R) which can be continued to entire functions of exponential type ⪯ ϕ, i.e. the classical Paley-Wiener class.

Keywords

Riesz basis entire functions tempered splines asymptotic relation 

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Copyright information

© Science in China Press 2000

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Normal UniversityBeijingChina

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