Fourier-Laguerre transform, convolution and wavelets on the ball

Дата и время публикации : 2013-07-04T12:43:00Z

Авторы публикации и институты :
J. D. McEwen
B. Leistedt

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 4 pages, 2 figures, Proceedings of 10th International Conference on Sampling Theory and Applications (SampTA), Codes are publicly available at http://www.s2let.org and http://www.flaglets.org
Первичная категория: cs.IT

Все категории : cs.IT, astro-ph.IM, math.IT

Краткий обзор статьи: We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function. We review the exact Fourier-Laguerre wavelet transform on the ball, coined flaglets, and show that flaglets constitute a tight frame.

Category: Physics