Abstract
In this paper we mainly discuss the uniform excess of frames in finite dimensional Hilbert spaces. We discuss the relationship between uniform excess frames and full spark frames, give several methods to construct uniform excess frames. We also show that every full spark frame has the full range property and the intersection dependent property, and is linearly connected. At the same time we give a sufficient condition for two uniform excess frames can be woven.
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Acknowledgements
We thank the anonymous referees for valuable suggestions and comments on constructing uniform frames and testing for uniform excess being NP-hard, which lead to a significant improvement of our manuscript.
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This work is partly supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2016J01014), the Key funded research projects of higher institutions of Henan province (Grant No. 17A110015), and the projects of Xiamen University of Technology (Grant No. G2017005).
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Xiao, X., Zhou, G. & Zhu, Y. Uniform Excess Frames in Hilbert Spaces. Results Math 73, 108 (2018). https://doi.org/10.1007/s00025-018-0871-0
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DOI: https://doi.org/10.1007/s00025-018-0871-0