Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical
random fields. The main emphasis is on tools from harmonic analysis, beginning with the …

In recent years, a rapidly growing literature has focussed on the construction of wavelet
systems to analyze functions defined on the sphere. Our purpose in this paper is to …

The construction of needlet-type wavelets on sections of the spin line bundles over the
sphere has been recently addressed in Geller and Marinucci (2008)[14], and Geller et …

We develop a needlet approach to estimate the amplitude of general (including non-
separable) bispectra and trispectra in the cosmic microwave background, and apply this to …

We consider the statistical analysis of random sections of a spin fibre bundle over the
sphere. These may be thought of as random fields that at each point p∈S^2 take as a value …

In this paper, Poisson wavelets on n n-dimensional spheres, derived from Poisson kernel,
are introduced and characterized. We compute their Gegenbauer expansion with respect to …

The construction of adaptive nonparametric procedures by means of wavelet thresholding
techniques is now a classical topic in modern mathematical statistics. In this paper, we …

A new construction of spin weighted wavelets on the sphere is presented in the paper. The
wavelets are similar to those derived from approximate identities but the constraints of the …

Spin weighted functions, introduced in 1966 by Newman and Penrose, are used primarily for
description of the cosmic microwave background radiation. In the present paper, an analysis …

This thesis collects some results on spherical wavelets and their applications to statistical
models concerning semiparametric and non-parametric estimation in the frequency domain …