Abstract
In this paper, we introduce a set of frame generators for a unitary system which is closed under linear combinations. Certain structural properties of the set are studied. Then we give several sufficient conditions such that an operator is a frame generator multiplier for certain unitary systems. Since there are two natural norms endowed with each Bessel multiplier, i.e., the usual operator norm and the Bessel norm, we compare these norms of Bessel multipliers for some cases.
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Funding was provided by CSC (Grant No. 201406985014).
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Communicated by Dr. Terhorst, Dr. Dmitry, Dr. Izchak and Prof. Alpay.
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Guo, X. Spaces of Bessel Generators and Characterizations of Bessel Generator Multipliers for Unitary Systems. Complex Anal. Oper. Theory 11, 811–823 (2017). https://doi.org/10.1007/s11785-016-0599-3
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DOI: https://doi.org/10.1007/s11785-016-0599-3