Author

G. Pfander

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Preprint Sep 2026

Schwartz-Class Gabor Windows and the Balian-Low Classification

A lattice Gabor frame consists of a window function and its time-frequency shifts along a lattice. We classify the lattices that admit Schwartz-class and, equivalently, Feichtinger frame windows. Except for symplectically irrational lattices of critical covolume 1,, we determine the lattice-dependent achievable window...

Andrei Caragea, G. Pfander · 0 citations

Preprint Aug 2026

Functions with comparable integrals on all k-planes

Let $d \ge 2$ and $1 \le k \le d-1$. We show that if $f:\mathbb{R}^d\to\mathbb{R}$ is nonnegative and measurable and $0<m\le M<\infty$ then it is impossible that on almost all affine $k$-planes $P$ in $\mathbb{R}^d$ the integral of $f$ on $P$ lies between $m$ and $M$. Let $G = \mathbb{Z}^k \times \{0\}^{d-k}$. Using $m...

Mihail N. Kolountzakis, G. Pfander · 0 citations