Geodesic
On R-dual of type III in Hilbert spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 62-74

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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. 
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     title = {On {R-dual} of type {III} in {Hilbert} spaces},
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H. Führ; J. Cheshmavar; A. Akbarnia. On R-dual of type III in Hilbert spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 62-74. http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a4/