English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This is a direct computation of the spectral representation of homogeneousspin-weighted spherical random fields with arbitrary integer spin. Itgeneralises known results from Cosmology for the spin-2 Cosmic MicrowaveBackground polarisation and Cosmic Shear fields, without decomposition into$E$- and $B$-modes. The derivation uses an instructive representation ofspin-weighted spherical functions over the Spin(3) group, where thetransformation behaviour of spin-weighted fields can be treated more naturallythan over the sphere, and where the group nature of Spin(3) greatly simplifiescalculations for homogeneous spherical fields. It is shown that i) differentmodes of spin-weighted spherical random fields are generally uncorrelated, ii)the usual definition of the power spectrum generalises, iii) there is a simplerelation to recover the correlation function from the power spectrum, and iv)the spectral representation is a sufficient condition for homogeneity of thefields.

The Spectral Representation of Homogeneous Spin-Weighted Random Fields on the Sphere