Orthogonal Fourier Analysis on Domains

Mihail N. Kolountzakis

Orthogonal Fourier Analysis on Domains

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arxiv 2408.15361 v3 pith:A7R6RWSE submitted 2024-08-27 math.CA math.MG

Mihail N. Kolountzakis This is my paper · ORCID

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In this paper we go over the history of the Fuglede or Spectral Set Conjecture as it has developed over the last 30 years or so. We do not aim to be exhaustive and we do not cover important areas of development such as the results on the problem in classes of finite groups or the version of the problem that focuses on spectral measures instead of sets. The selection of the material has been strongly influenced by personal taste, history and capabilities. We are trying to be more descriptive than detailed and we point out several open questions.

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Spectrality of a measure consisting of two line segments
math.CA 2025-01 accept novelty 8.0 of 10

For the measure on two crossed segments with endpoint offset t, the paper proves non-spectrality for all shifts strictly between -1/2 and 0 and for all irrational shifts, leaving only t=-1/2 open.

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