The empirical process on Gaussian spherical harmonics

THE EMPIRICAL PROCESS ON GAUSSIAN SPHERICAL HARMONICS By Domenico Marinucci 1 and Mauro Piccioni

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaus-sianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literatur...

Spherical Harmonics

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

On a spherical code in the space of spherical harmonics

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

3 Generalized Spherical Harmonics

Optimal Spherical Harmonics Projection

We introduce the reader to the mathematics behind projection of n-dimensional vectors into a basis on n-dimensional space, where n can be anything upto and including infinity. We show how ideally one wants to project into the duals of a basis if this basis is not orthonormal, and provide the mathematics to formulate this operation in matrix form. The second part of the article discusses spheric...