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The Journal of Geometric Analysis

, Volume 16, Issue 4, pp 585–596 | Cite as

Riesz sequences of translates and generalized duals with support on [0, 1]

  • O. ChristensenEmail author
  • H. O. Kim
  • R. Y. Kim
  • J. K. Lim
Article

Abstract

If the integer translates of a function ø with compact support generate a frame for a subspace W of L 2(ℝ),then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether ø is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists.

Math Subject Classifications

42C15 

Key Words and Phrases

Frames of translates dual frame dual generator short support 

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Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  • O. Christensen
    • 1
    Email author
  • H. O. Kim
    • 2
  • R. Y. Kim
    • 3
  • J. K. Lim
    • 4
  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark
  2. 2.Division of Applied MathematicsKAISTDaejeonRepublic of Korea
  3. 3.Department of MathematicsYeungnam UniversityGyeongsangbuk-doRepublic of Korea
  4. 4.Department of Computational Mathematics and InformaticsHankyong National UniversityKyonggi-DoRepublic of Korea

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