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Dilations of dual g-frame generators for an abstract wavelet system

Author

Listed:
  • Liang Li

    (Nanjing Audit University)

  • Pengtong Li

    (Nanjing University of Aeronautics and Astronautics)

Abstract

In this paper, we study the dilation of g-frame generators and the dual g-frame generators for an abstract wavelet system. By the semi-orthogonality of a special unitary system, we prove the dual g-frame generators can be dilated to a pair of dual g-Riesz basis generators for some larger Hilbert space. We first show the existence of the dual g-frame generators with the same structure of a g-frame generator for a unitary system. We then get a sufficient and necessary condition for the existing of the dual g-frame generators for unitary groups on a subspace.

Suggested Citation

  • Liang Li & Pengtong Li, 2020. "Dilations of dual g-frame generators for an abstract wavelet system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 589-610, June.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0419-3
    DOI: 10.1007/s13226-020-0419-3
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