Family of Frames (Journal of Informatics and Mathematical Sciences, 2017)
We introduce here the concept of Family of Frames, a new type of generator systems for Hilbert separable spaces. These families, similar to frames and bases, allow the representation of all vectors of the space through a process of analysis, and reconstruction of them by a process of synthesis. These families are dened using the concept of outer frame of a closed subspace. These new systems are even less restrictive than the known frames. In addition, this new concept has a particular characteristic for some multiresolution analysis (MRA), which is the ability to represent any vector of the space from the generators of the subspacesof MRA, without needing to build wavelets frames associated to the MRA for this end.
Keywords: Frames; Dual frames; Outer frame; Analysis; Synthesis; Multiresolution analysis