In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

Frame theory is an active research area in mathematics, computer science and engineering with many exciting applications a variety of different fields. In this paper we study the notion dual continuous K-frames Hilbert spaces. Also establish some properties.

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L(R ) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connectio...