Zugl.: Karlsruhe, Univ., Diss., 2009 / Hergestellt on demand

Zugl.: Göttingen, Univ., Diss., 2008

In the presented work, we study several basis systems satisfying certain spatial/spectral localization conditions on the unit sphere and the ball embedded in Euclidean space of dimension $d\geq2$. For the spherical setup, we investigate some properties of the Hardy-Hodge decomposition for locally supported fields, and propose a multi-scale basis system that is suitable for modeling the Hardy components of such spherical vector fields and allows a simple mapping between the Hardy spaces. In the case of the solid ball, we revisit the Slepian spatiospectral concentration problems for the spherical Fourier-Jacobi, spherical Fourier-Bessel, as well as the multivariate algebraic polynomial systems. We investigate the bimodal distribution phenomena of the eigenvalues of concentration operators and give an asymptotic characterization of the Shannon number for these setups, which lay a foundation for the utilization of associated Slepian bases and localized spectral analysis.