16 papers
Wavelet based solutions to the Poisson and the Helmholtz equations on the -dimensional unit sphere
Ilona Iglewska-Nowak, Piotr Stefaniak
We present a method of solving partial differential equations on the -dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate id…
Wavelet methods in partial differential equations on spheres
{Ilona Iglewska-Nowak, Piotr Stefaniak
We propose a method of solving partial differential equations on the -dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate i…
Uncertainty product of the spherical Abel-Poisson wavelet
Ilona Iglewska-Nowak
In the present paper, the variances in the space and momentum domains of the spherical Abel-Poisson wavelet, as well as the limit of the uncertainty product for , where …
Uncertainty product of the spherical Gauss-Weierstrass wavelet
Ilona Iglewska-Nowak
In this paper, asymptotic behavior of the uncertainty product of Gauss-Weierstrass wavelet is investigated. It is shown that the uncertainty product is bounded from above, a featur…
A continuous spherical wavelet transform for~
Ilona Iglewska-Nowak
In the present paper, a wavelet family over the -dimensional sphere is constructed such that for each scale the wavelet is a polynomial and the inverse wavelet transform of a co…
On the uncertainty product of spherical functions
Ilona Iglewska-Nowak
The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the…