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<p>We obtain the estimates from below and above for the average decay of Fourier transform of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha_1,\alpha_2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Ahlfors regular measure. As an application, we obtain the upper bound of Beurling dimension of frame spectra for a class of Moran measures.</p>

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A remark on the average decay of Fourier transform for regular measures

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • J. Li,
  • S. Luo,
  • Z. Wu

摘要

We obtain the estimates from below and above for the average decay of Fourier transform of \((\alpha_1,\alpha_2)\) ( α 1 , α 2 ) -Ahlfors regular measure. As an application, we obtain the upper bound of Beurling dimension of frame spectra for a class of Moran measures.