Title :
Gabor transformation on the circle
Author_Institution :
Dept. of Math., Univ. of Toyama, Toyama, Japan
Abstract :
In [2] and [3], we considered the Gabor transform of analytic functionals on the sphere in general dimension and we expressed it by a series expansion with the spherical harmonics and the Bessel functions. In this paper, following our previous results, we will consider the Gabor transform of analytic functionals, especially of square integrable functions on the circle (2-dimensional sphere), in more detail. Then we will construct the inverse Gabor transformation explicitly.
Keywords :
Bessel functions; Fourier transforms; geometry; integral equations; inverse transforms; series (mathematics); 2D sphere; Bessel functions; Fourier transform; analytic functionals; inverse Gabor transformation; series expansion; spherical harmonics; square integrable functions; Fourier transforms; Harmonic analysis; Pattern recognition; Polynomials; Wavelet analysis; Wavelet transforms; Gabor transformation; series expansion; spherical harmonics;
Conference_Titel :
Wavelet Analysis and Pattern Recognition (ICWAPR), 2014 International Conference on
Conference_Location :
Lanzhou
Print_ISBN :
978-1-4799-4212-1
DOI :
10.1109/ICWAPR.2014.6961302
