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.
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This work is supported by National Natural Science Foundation of China (Nos. 11671201 and 11771379).
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Li, L., Li, P. Dilations of dual g-frame generators for an abstract wavelet system. Indian J Pure Appl Math 51, 589–610 (2020). https://doi.org/10.1007/s13226-020-0419-3
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DOI: https://doi.org/10.1007/s13226-020-0419-3