On the Fourier transforms of self-similar measures

2012/12/07 by Masato Tsujii, Tsujii, Masato · 1 citation
Computer Science · Mathematics · #28A80 #42A38 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1212.1553

openalex publication_date 2012/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the Fourier transform Fμ of a general (non-trivial) self-similar measure μ on the real line ℝ, we prove a large deviation estimate lim_{c→ +0} \varlimsup_{t→ ∞}(1)/(t)log (Leb\x∈ [-e^t, e^t]| |Fμ(ξ)| ≥ e^-ct \)=0.

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