5 papers · 1 filter
Approximately dual pairs of wavelet frames
Ana Benavente, Ole Christensen, Marzieh Hasannasab +3
This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}ψ( a^j\cdot -kb)\}_{j,k\in \mathbb Z}…
B-spline approximations of the Gaussian, their Gabor frame properties, and approximately dual frames
Ole Christensen, Hong Oh Kim, Rae Young Kim
We prove that Gabor systems generated by certain scaled B-splines can be considered as perturbations of the Gabor systems generated by the Gaussian, with a deviation within an arbi…
On partition of unities generated by entire functions and Gabor frames in $\ltrd$ and $\ell^2(\mzd)$
Ole Christensen, Hong Oh Kim, Rae Young Kim
We characterize the entire functions of variables, for which the $\mzd$-translates of satisfy the partition of unity for some $N\in \mn.$ In contra…
On the Gabor frame set for compactly supported continuous functions
Ole Christensen, Hong Oh Kim, Rae Young Kim
We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval…
On Gabor frames generated by sign-changing windows and B-splines
Ole Christensen, Hong Oh Kim, Rae Young Kim
For a class of compactly supported windows we characterize the frame property for a Gabor system $\mts,$ for translation parameters belonging to a certain range depending on th…