SOME PROPERTIES OF FOURIER QUASICRYSTALS AND MEASURES ON A STRIP

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Favorov S., DEĞER Ö.

Matematychni Studii, cilt.66, sa.1, ss.97-104, 2026 (Scopus)

Özet

We extend certain results of the theory of Fourier quasicrystals on the real line to the case of a horizontal strip of finite width. We define the Fourier transform for measures on a strip that is a natural generalization of the Fourier transform for measures on the line. For positive or translation bounded measures μ on a strip with the Fourier transform of the form û = ∑γ∈Γ bγδγ we prove that the measure ν = ∑γ∈Γ |bγ|2 δγ has the exponential growth. If for some η > 0 the points of Γ in every interval of length η are linearly independent over integers then the measure û also has the exponential growth.