We study the asymptotic behavior of the quadratic means on spheres of increasing radius of the Fourier transforms of characteristic functions of sets with smooth boundary. Beside to give different proofs of known Euclidean results, we also consider the non-Euclidean Fourier transform on the two dimensional sphere and the hyperbolic disk
Brandolini, L., Colzani, L., Torlaschi, A. (2001). Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces. TOHOKU MATHEMATICAL JOURNAL, 53(3), 467-478 [10.2748/tmj/1178207421].
Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces
Colzani, L;
2001
Abstract
We study the asymptotic behavior of the quadratic means on spheres of increasing radius of the Fourier transforms of characteristic functions of sets with smooth boundary. Beside to give different proofs of known Euclidean results, we also consider the non-Euclidean Fourier transform on the two dimensional sphere and the hyperbolic diskFile in questo prodotto:
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