Fourier uniqueness pairs of powers of integers

2019/10/09 by Ramos, João P. G., Sousa, Mateus · 2 citations
#42A38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.04276

Abstract

We prove, under certain conditions on (α,β), that each Schwartz function f such that f(± n^α) = f(± n^β) = 0, ∀ n ≥ 0 must vanish identically, complementing a series of recent results involving uncertainty principles, such as the pointwise interpolation formulas by Radchenko and Viazovska and the Meyer-Guinnand construction of self-dual crystaline measures.

Cited by

• Critical and asymmetric Fourier uniqueness pairs
• Spectral Criteria for Uniqueness Pairs of Unitary Transforms

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