A NOTE ON DISCRETE FRAMES OF TRANSLATES IN CN

Year 2016, Volume: 6 Issue: 1, 143 - 149, 01.06.2016

- Deepshikha L. K. Vashisht

Abstract

In this note, we present necessary and sufficient conditions with explicit frame bounds for a discrete system of translates of the form {Tkφ}k∈ZN to be a frame for the unitary space C N .

Keywords

Frame, frames of translates, discrete system in C N .

References

• Benedetto,J. and Li,S., (1998), The theory of multiresolution analysis frames and applications to filter banks, Appl. Comp. Harm. Anal., 5, pp. 389-427.
• Casazza,P.G. and Kutyniok,G., (2012), Finite Frames: Theory and Applications, Birkh¨auser.
• Christensen,O., (2002), An Introduction to Frames and Riesz Bases, Birkh¨auser, Boston .
• Christensen,O., Deng,B. and Heil,C., (1999), Density of Gabor frames, Appl. Comp. Harm. Anal., 7 , pp. 292-304.
• Daubechies,I., (1992), Ten Lectures on Wavelets, SIAM, Philadelphia.
• Deepshikha and Vashisht,L.K., (2015), Necessary and sufficient conditions for discrete wavelet frames in CN, submitted.
• Pfander,G.E., (2012), Gabor frames in finite dimensions, In: Finite Frames: Theory and Applications, Birkh¨auser, pp. 193-239.
• Vashisht,L.K. and Deepshikha, Discrete wave packet frames in CN, under preparation.