Dual Fusion Frames

ANA BENAVENTE; SIGRID HEINEKEN; PATRICIA MORILLAS; MARÍA ZAKOWICZ

Córdoba

Congreso; CLAM 2012, IV Congreso Latinoamericano de Matemáticos; 2012

In many applications such as distributing sensing, parallel processing and packet encoding, a distributed processing by combining locally data vectors has to be implemented. Fusion frames (or frames for subspaces) are a generalization of frames and provide a mathematical framework suitable for these applications. They are collections of weights and orthogonal projections, and permit us to recover an element of a Hilbert space from packets of linear coefficients. The definition of dual fusion frames presents some technical problems, related to the domain of the synthesis operator. The definition commonly used is the analogous to the canonical dual in the classical frame theory. We define a new concept of dual, that extends this notion and overcomes these technical difficulties. We present a characterization of these new duals.