Family of Frames

María Luisa Gordillo

Abstract


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 subspaces
of MRA, without needing to build wavelets frames associated to the MRA for this end.


Keywords


Frames; Dual frames; Outer frame; Analysis; Synthesis; Multiresolution analysis

Full Text:

PDF

References


L.Baggett, H. Medina and K. Merrill, Generalized multi-resolution analyses and a construction procedure for all wavelet sets in Rn, Journal Journal of Fourier Analysis and Applications. Publisher Birkhuser, Boston, 5 (1999), 1531-5851.

J.J. Benedetto and O. Treiber, Wavelets frames: multiresolution and extension principles. Wavets trasnforms and time frequency signal analysis. (ed. Debanath,L) Birkausser, Boston(2001), 1-36.

C. Cabrelli, M. L. Gordillo, Existence of multiwavelets in Rn. Proc. Amer. Math. Soc. 130, 5 (2002), 1413-1424.

R.J. Duffin and A.C Schaeuer, A class of nonharmonic Fourier Series, Trans.Amer.Math.Soc., 72 (1952), 341{366.

S. Li and H. Ogawa, A theory of pseudoframes for subspaces with applications, Tech. report, (1998).

S. Mallat, Multiresolution approximation and wavelets, Trans. Amer. Math. Soc. 315 (1989).




DOI: http://dx.doi.org/10.26713%2Fjims.v9i1.610

eISSN 0975-5748; pISSN 0974-875X