8th International Conference on
Computational Harmonic Analysis

September 12-16, 2022

Ingolstadt, Germany

"Symmetric Duality in Fusion Frames"

Shamsabadi, Mitra

Several generalizations of frames were proposed which share many analogue properties of ordinary frames. Duality, which plays a key role in theory and applications, is usually symmetric for many of those classes. In fusion frame theory, some results are the equivalent of frame theory ones, but this is not true for duality. The mismatch of the coefficient spaces of different systems necessitates new approaches and definitions, and that is why the symmetric property is hurt. In this talk, we study fusion frame duality and are interested to find some conditions under which the duality of two fusion frames is symmetric. We will state that the duality for every fusion Riesz basis and its canonical dual is symmetric. Moreover, for fusion Riesz bases, we give a formula for the frame operator of their canonical duals.

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