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- W4295698778 abstract "A set $Omega subset mathbb{R}^d$ is said to be spectral if the space $L^2(Omega)$ admits an orthogonal basis of exponential functions. Fuglede (1974) conjectured that $Omega$ 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 $mathbb{R}^d$. 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." @default.
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- W4295698778 date "2022-09-09" @default.
- W4295698778 modified "2023-10-18" @default.
- W4295698778 title "Spectral sets and weak tiling" @default.
- W4295698778 doi "https://doi.org/10.48550/arxiv.2209.04540" @default.
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