info:eu-repo/semantics/article
Duality in reconstruction systems
Fecha
2012-02Registro en:
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Duality in reconstruction systems; Elsevier Science Inc; Linear Algebra and its Applications; 436; 3; 2-2012; 447-464
0024-3795
CONICET Digital
CONICET
Autor
Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
Resumen
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 study the structure of the minimizers of this functional. In the case of irreducible RS's the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.