Spectral sets and weak tiling

Kolountzakis, Mihail N. and Lev, Nir and Matolcsi, Máté (2023) Spectral sets and weak tiling. SAMPLING THEORY, SIGNAL PROCESSING, AND DATA ANALYSIS, 21 (2). ISSN 2730-5716 (print); 2730-5724 (online)

Preview

Text 2209.04540v3.pdf Download (249kB) | Preview

Abstract

A set Ω ⊂ Rd is said to be spectral if the space L2(Ω) admits an orthogonal basis of exponential functions. Fuglede (1974) conjectured that Ω is spectral if and only if it can tile the space by translations. While this conjecture was disproved for general sets, it was recently proved that the Fuglede conjecture does hold for the class of convex bodies in Rd. The proof was based on a new geometric necessary condition for spectrality, called “weak tiling”. In this paper we study further properties of the weak tiling notion, and present applications to convex bodies, non-convex polytopes, product domains and Cantor sets of positive measure.

Actions (login required)

Edit Item