\(L^p\)-integrability, dimensions of supports of Fourier transforms and applications

DOI10.1007/s00041-014-9334-5zbMath1307.42009arXiv1306.4494OpenAlexW1985993032MaRDI QIDQ485264

K. S. Senthil Raani

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4494

zbMATH Keywords

Hausdorff dimensionSalem setspacking measureAhlfors-David regular setssupports of Fourier transformsWiener-Tauberian theorems

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Hausdorff and packing measures (28A78) Tauberian theorems (40E05)

Related Items (1)

\(L^p\)-Fourier asymptotics, Hardy-type inequality and fractal measures

Cites Work

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• Wiener's `closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon
• \(L^{p}\) Wiener-Tauberian theorems for \(M(2)\)
• Asymptotic properties of solutions of differential equations with simple characteristics
• \(L^p\)-integrability, supports of Fourier transforms and uniqueness for convolution equations
• The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem
• The density theorem and Hausdorff inequality for packing measure in general metric spaces
• On a closure problem
• On singular monotonic functions whose spectrum has a given Hausdorff dimension
• A Note on the Span of Translations in L p
• Tauberian theorems

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