9 citations · 11 across the 10 of their papers we have counts for
13 papers
Some unexpected behaviors of operators with small time-frequency dispersion
Dae Gwan Lee
We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighbo…
Bases of complex exponentials with restricted supports
Dae Gwan Lee, Goetz E. Pfander, David Walnut
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintaine…
Unions of exponential Riesz bases
Dae Gwan Lee
We develop new methods for constructing exponential Riesz bases by taking unions of exponential Riesz bases. These methods are based on taking unions of frequency sets and domains…
A note on exponential Riesz bases
Andrei Caragea, Dae Gwan Lee
We prove that if , , are disjoint intervals in with the property that the numbers are l…
On construction of bounded sets not admitting a general type of Riesz spectrum
Dae Gwan Lee
Despite the recent advances in the theory of exponential Riesz bases, it is yet unknown whether there exists a set which does not admit a Riesz spectrum, m…
A note on the invertibility of the Gabor frame operator on certain modulation spaces
Dae Gwan Lee, Friedrich Philipp, Felix Voigtlaender
We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space , the weighted…
Quantitative approximation results for complex-valued neural networks
A. Caragea, D. G. Lee, J. Maly +2
Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued n…
Time-Frequency Shift Invariance of Gabor Spaces with an -Generator
Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1
We consider Gabor Riesz sequences generated by a lattice and a window function which is well localized in both time and frequency. W…
A quantitative subspace Balian-Low theorem
Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1
Let be the subspace spanned by a Gabor Riesz sequence with and a lattice of rational density.…
Binary Compressive Sensing via Smoothed Gradient Descent
Tianlin Liu, Dae Gwan Lee
We present a Compressive Sensing algorithm for reconstructing binary signals from its linear measurements. The proposed algorithm minimizes a non-convex cost function expressed as…
A Balian-Low Theorem for Subspaces
A. Caragea, D. Lee, G. E. Pfander +1
We extend the Balian-Low theorem to Gabor subspaces of by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a…
Time-frequency shift invariance of Gabor spaces generated by integer lattices
Carlos Cabrelli, Dae Gwan Lee, Ursula Molter +1
We study extra time-frequency shift invariance properties of Gabor spaces. For a Gabor space generated by an integer lattice, we state and prove several characterizations for its t…
Compressed Sensing for Finite-Valued Signals
Sandra Keiper, Gitta Kutyniok, Dae Gwan Lee +1
The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engin…