Abstract:
Following work by Casazza, Kutyniok, and Lammers and its development by
Stoeva and Christensen, we provide some
novel characterizations of R-dual sequences of type III in Hilbert spaces.
We systematically extend the construction procedure by basing it on a
choice of an antiunitary involution. For certain
classes of R-duals of type III, we derive a representation
of the associated frame operator in terms of spectral measures.
Keywords:frames, Riesz sequence, Riesz basis, spectral
representation, R-dual of type I, R-dual of type III.