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

Liang Li () and Pengtong Li ()
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Liang Li: Nanjing Audit University
Pengtong Li: Nanjing University of Aeronautics and Astronautics

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 589-610

Abstract: 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.

Keywords: Frames; G-frames; G-frame generators; G-dual; dilations; unitary system; 42C15; 46L10; 42C40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0419-3

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