Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real
Line, the Sphere, and the Ball focuses on spherical problems as they occur in the …

Many areas of science and engineering encounter data defined on spherical manifolds.
Modelling and analysis of spherical data often necessitates spherical harmonic transforms …

We develop an exact wavelet transform on the three-dimensional ball (ie on the solid
sphere), which we name the flaglet transform. For this purpose we first construct an exact …

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a
signal can be probed not only in scale and position but also in orientation. Furthermore, a …

Spherical needlets are highly localized radial polynomials on the sphere S d⊂ R d+ 1, d≥
2, with centers at the nodes of a suitable cubature rule. The original semidiscrete spherical …

Inverse problems occur in many fields of geophysics, wherein surface observations are used
to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness …

The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-
posed problem. Smoothing constraints are widely employed to estimate a regularized …

This paper considers filtered polynomial approximations on the unit sphere S^ d ⊂ R^ d+ 1
S d⊂ R d+ 1, obtained by truncating smoothly the Fourier series of an integrable function f …

This work presents the construction of a novel spherical wavelet basis designed for
incomplete spherical datasets, ie datasets which are missing in a particular region of the …

We formulate and solve the analog of Slepian spatial-spectral concentration problem on the
three-dimensional ball. Both the standard Fourier–Bessel and also the Fourier–Laguerre …