On R-duals of type III in Hilbert spaces (Q2667880)

Following work by Casazza, Kutyniok, and Lammers [\textit{P.~G. Casazza} et al., J. Fourier Anal. Appl. 10, No.~4, 383--408 (2004; Zbl 1058.42020)] and its development by Stoeva and Christensen [\textit{D.~T. Stoeva} and \textit{O.~Christensen}, J. Fourier Anal. Appl. 21, No.~2, 383--400 (2015; Zbl 1312.42037)], some novel characterizations of R-dual sequences of type~III in Hilbert spaces are provided. The construction procedure is based on a choice of an antiunitary involution is systematically extended. For certain classes of R-duals of type~III, a representation of the associated frame operator in terms of spectral measures is derived.