2 citations · 2 across the 14 of their papers we have counts for
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Fuglede's conjecture holds for three intervals
Ruxi Shi
We prove that every bounded measurable subset of the real line that is both spectral and a union of three intervals tiles the line by translations, thereby completing Fuglede's con…
Spectra for finite unions of line segments
Mihail N. Kolountzakis, Ruxi Shi, Sha Wu
In this paper we study the spectrality of arc-length measures supported on the union of two line segments in the plane. We show that any such spectral measure must admit a line spe…
When is the fractal uncertainty principle for discrete Cantor sets most uncertain?
Chun-Kit Lai, Ruxi Shi
We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as…
On dimensions of frame spectral measures and their frame spectra
Ruxi Shi
In this paper, we prove that the entropy dimension of a frame spectral measure is superior than or equal to the Beurling dimension of its frame spectrum.
Equi-distributed property and spectral set conjecture on
Ruxi Shi
In this paper, we show an equi-disctributed property in -dimensional finite abelian groups where is a prime number. By using this equ…
Fuglede's conjecture holds on cyclic groups
Ruxi Shi
Fuglede's spectral set conjecture states that a subset of a locally compact abelian group tiles the group by translation if and only if there exists a subset of continuous…