Density Results for Continuous Frames

Some results on continuous frames for Hilbert Spaces

Generalized Continuous Frames for Operators

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

some results on continuous frames for hilbert spaces

Density results for frames of exponentials

For a separated sequence Λ = {λk}k∈Z of real numbers there is a close link between the lower and upper densities D−(Λ), D(Λ) and the frame properties of the exponentials {ek}k∈Z: in fact, {ek}k∈Z is a frame for its closed linear span in L(−γ, γ) for any γ ∈]0, πD−(Λ)[∪]πD+(Λ),∞[. We consider a classical example presented already by Levinson [10] with D−(Λ) = D(Λ) = 1; in this case, the frame pr...

Continuous frames and g-frames

In this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by Ali et al‎. ‎in 1993‎. ‎Indeed‎, ‎it is shown that these generalizations can be considered as an operator between two Hilbert spaces‎.