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Pairs of oblique duals in spaces of periodic functions

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Abstract

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials.

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Article 03 December 2014

Yoo Young Koo & Jae Kun Lim

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Denmark, Building 303, 2800, Lyngby, Denmark

    Ole Christensen

  2. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260, Republic of Singapore

    Say Song Goh

Authors
  1. Ole Christensen
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  2. Say Song Goh
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Correspondence to Ole Christensen.

Additional information

Communicated by Qiyu Sun.

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Christensen, O., Goh, S.S. Pairs of oblique duals in spaces of periodic functions. Adv Comput Math 32, 353–379 (2010). https://doi.org/10.1007/s10444-009-9115-x

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  • DOI: https://doi.org/10.1007/s10444-009-9115-x

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