arXiv subjects

Yurii I. Lyubarskii

Publications and source records attributed to Yurii I. Lyubarskii.

2 recordsLinked to original sources

arXiv2008

Phase space distribution of Gabor expansions

We present an example of a complete and minimal Gabor system consisting of time-frequency shifts of a Gaussian, localized at the coordinate axes in the time-frequency plane (phase space). Asymptotically, the number of time-frequency shifts contained in a disk centered at the origin is only 2/pi times the number of points from the von Neumann lattice found in the same disk. Requiring a certain regular distribution in phase space, we show that our system has minimal density among all complete and minimal systems of time-frequency shifts of a Gaussian.

math.FA↗

arXiv1995

Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's $(A_p)$ condition

We describe the complete interpolating sequences for the Paley-Wiener spaces $L^p_π$ ($1<p<\infty$) in terms of Muckenhoupt's $(A_p)$ condition. For $p=2$, this description coincides with those given by Pavlov (1979), Nikol'skii (1980), and Minkin (1992) of the unconditional bases of complex exponentials in $L^2(-π,π)$. While the techniques of these authors are linked to the Hilbert space geometry of $L^2_π$, our method of proof is based on turning the problem into one about boundedness of the Hilbert transform in certain weighted $L^p$ spaces of functions and sequences.

math.FA↗