Fuglede's conjecture holds in ${\mathbb{Q}}_p$

Abstract

Fuglede's conjecture in ${\mathbb{Q}}_p$ is proved. That is to say, a Borel set of positive and finite Haar measure in ${\mathbb{Q}}_p$ is a spectral set if and only if it tiles ${\mathbb{Q}}_p$ by translation.

24 pages

References in corpus (4)

• Complex Hadamard matrices and the Spectral Set Conjecture
• Tiling sets and spectral sets over finite fields
• Compact Open Spectral Sets In ${\mathbb{Q}}_p$
• Bounded tiles in ${\mathbb{Q}}_p$ are compact open sets

Cited by in corpus (3)

• Equi-distributed property and spectral set conjecture on ${\mathbb{Z}}_{p^2}\times {\mathbb{Z}}_p$
• Convolution Idempotents with a given Zero-set
• Compact Open Spectral Sets In ${\mathbb{Q}}_p$