Characterization of Alternate Duals of Continuous Frames and Representation Frames
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We give a new characterization of alternate dual of continuous frames and then apply these results to representation frames which are generated by a unitary representation on a locally compact group. We also investigate under which conditions alternate duals can be reduced to the canonical dual. Finally, we introduce representation frames with a unique representation form dual and obtain more results on alternate (not necessary representation form) duals.
KeywordsDual frames continuous frames unitary representation representation frames
Mathematics Subject ClassificationPrimary 42C15 Secondary 20C99
- 18.Han, D., Larson, D., Liu, B., Liu, R.: Operator-valued measures, Dilations, and the Theory of Frames. Mem. Am. Math. Soc. 229(1075), (2014)Google Scholar