28 citations · 82 across the 14 of their papers we have counts for
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…
Spin weighted wavelets on the sphere
Ilona Iglewska-Nowak
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of param…
Uncertainty product of spherical wavelets
Ilona Iglewska-Nowak
In the paper, asymptotic behavior of the uncertainty product for a family of zonal spherical wavelets is computed. The family contains the most popular wavelets, such as Gauss-Weie…
Uncertainty of Poisson wavelets
Ilona Iglewska-Nowak
Poisson wavelets are a powerful tool in analysis of spherical signals. In order to have a deeper characterization of them, we compute their uncertainty product, a quantity introduc…
Angular multiselectivity with spherical wavelets
Ilona Iglewska-Nowak
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to f…
Multiresolution on n-dimensional spheres
Ilona Iglewska-Nowak
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing an…
Directional wavelets on -dimensional spheres
Ilona Iglewska-Nowak
Directional Poisson wavelets, being directional derivatives of Poisson kernel, are introduced on -dimensional spheres. It is shown that, slightly modified and together with anot…
Semi-continuous and discrete wavelet frames on -dimensional spheres
Ilona Iglewska-Nowak
The paper shows that under some mild conditions -dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dens…
Poisson wavelets on -dimensional spheres
Ilona Iglewska-Nowak
In this paper, Poisson wavelets on -dimensional spheres, derived from Poisson kernel, are introduced and characterized. We compute their Gegenbauer expansion with respect to the…
Continuous wavelet transforms on -dimensional spheres
Ilona Iglewska-Nowak
In this paper, we are concerned with -dimensional spherical wavelets derived from the theory of approximate identities. For nonzonal bilinear wavelets introduced by Ebert \emph{…
Frames of directional wavelets on -dimensional spheres
Ilona Iglewska-Nowak
The major goal of the paper is to prove that discrete frames of (directional) wavelets derived from an approximate identity exist. Additionally, a kind of energy conservation prope…