Work

Geometric implications of weak tiling

Year: 2025

Type: article

Abstract: The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling and establish some geometric properties of sets that weakly tile their complement. If $$A \subset \mathbb{R}^d$$ A ⊂ R d is a convex polytope, we give a direct and self-contained proof that A must be symmetric and have symmetric facets. If $$A \subset \mathbb{R}$$ A ⊂ R is a finite union of intervals, we give a necessary condition on the lengths of the gaps between the intervals.

Source: Analysis Mathematica

DOI: 10.1007/s10476-025-00121-5

Authors: M. N. Kolountzakis, N. Lev, M. Matolcsi

Institutions: University of Crete, Foundation for Research and Technology Hellas, Bar-Ilan University, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest University of Technology and Economics

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Israel Science Foundation