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pro vyhledávání: '"52C23"'
Autor:
Ulanovskii, Alexander, Zlotnikov, Ilya
Let $V^p_\Gamma(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $\Gamma$-shifts of a function $\mathcal{G}$, where $\Gamma\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$,
Externí odkaz:
http://arxiv.org/abs/2410.08682
Autor:
Grepstad, Sigrid
We show that given a lattice $\Gamma \subset \mathbb{R}^m \times \mathbb{R}^n$, and projections $p_1$ and $p_2$ onto $\mathbb{R}^m$ and $\mathbb{R}^n$ respectively, cut-and-project sets obtained using Jordan measurable windows $W$ and $W'$ in $\mathb
Externí odkaz:
http://arxiv.org/abs/2409.05450
Autor:
Favorov, Serhii
We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets of expone
Externí odkaz:
http://arxiv.org/abs/2408.09563
We study periodic approximations of aperiodic Schr\"odinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We characterize co
Externí odkaz:
http://arxiv.org/abs/2408.09282
The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was disproved
Externí odkaz:
http://arxiv.org/abs/2408.02151
In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions i
Externí odkaz:
http://arxiv.org/abs/2407.11184
Autor:
Baake, Michael, Mañibo, Neil
The sets of $\cB$-free integers are considered with respect to (reversing) symmetries. It is well known that, for a large class of them, the centraliser of the associated $\cB$-free shift (otherwise known as its automorphism group) is trivial. We ext
Externí odkaz:
http://arxiv.org/abs/2406.15242
Autor:
Perryman, Abigail, Sadun, Lorenzo
The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology $\check H^1(\Omega)$ gives upper and lower bounds for the size of the return module. For a
Externí odkaz:
http://arxiv.org/abs/2406.07501
We present a categorical formalism for context-free languages with morphisms given by correspondences obtained from rational transductions. We show that D0L-systems are a special case of the correspondences that define morphisms in this category. We
Externí odkaz:
http://arxiv.org/abs/2405.12485
Autor:
Berthé, Valérie, Yassawi, Reem
Aperiodic order refers to the mathematical formalisation of quasicrystals. Substitutions and cut and project sets are among their main actors; they also play a key role in the study of dynamical systems, whether they are symbolic, generated by tiling
Externí odkaz:
http://arxiv.org/abs/2404.04116