Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces

Authors
Brandolini, L Colzani, L Torlaschi, A
Citation
L. Brandolini et al., Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces, TOHOKU MATH, 53(3), 2001, pp. 467-478
Citations number
18
Categorie Soggetti
Mathematics
Journal title
TOHOKU MATHEMATICAL JOURNAL
ISSN journal
00408735 → ACNP
Volume
53
Issue
3
Year of publication
2001
Pages
467 - 478
Database
ISI
SICI code
0040-8735(200109)53:3<467:MSDOFT>2.0.ZU;2-B
Abstract
We study the asymptotic behavior of the quadratic means on spheres of incre asing radius of the Fourier transforms of characteristic functions of sets with smooth boundary. Beside to give different proofs of known Euclidean re sults, we also consider the non-Euclidean Fourier transform on the two dime nsional sphere and the hyperbolic disk.