2015/02/22 by Mihail N. Kolountzakis, Kolountzakis, Mihail N.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.CA
paper · pdf · doi:10.48550/arxiv.1502.06283
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openalex publication_date 2015/02/22 · arxiv created 2015/05/27 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a simple proof of the fact that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson Summation Formula finitely many times. More specifically the support of both the measure and its Fourier Tranform are not contained in a finite union of arithmetic progressions.