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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper presents theoretical analysis and software implementation for realharmonics analysis on the special orthogonal group. Noncommutative harmonicanalysis for complex-valued functions on the special orthogonal group has beenstudied extensively. However, it is customary to treat real harmonic analysisas a special case of complex harmonic analysis, and there have been limitedresults developed specifically for real-valued functions. Here, we develop aset of explicit formulas for real-valued irreducible unitary representations onthe special orthogonal group, and provide several operational properties, suchas derivatives, sampling, and Clebsch-Gordon coefficients. Furthermore, weimplement both of complex and real harmonics analysis on the special orthogonalgroup into an open source software package that utilizes parallel processingthrough the OpenMP library. The efficacy of the presented results areillustrated by benchmark studies and an application to spherical shapematching.

Real Harmonic Analysis on the Special Orthogonal Group