Duality in reconstruction systems

P. MASSEY; M. RUIZ; D. STOJANOFF

Braunschweig

Congreso; 17th International Linear Algebra Society Conference; 2011

In this talk, we consider reconstruction systems (RS´s), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS´s. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS´s, called the joint potential, and we study the structure of the minimizers of this functional. In the case of irreducible RS´s the minimizers are characterized as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. \ This contribution is joint work with Pedro Massey (UNLP-IAM, Argentina) and Demetrio Stojanoff (UNLP-IAM, Argentina).