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.

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

In order to improve the technology of cocoon processing, create waste-free technologies, a surface activator was synthesized on basis bardo residue fraction and lubricating oils formed during production ethyl alcohol. Based IR-spectral analysis, presence hydroxyl carboxyl groups in surfactants determined be suitable raw material for surfactants, substance from it can used staining. IR-spectrum ...

in this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for l^2(r^d). further, we illustrate our results with some examples and applications.