Equivalence between Modulus of Smoothness and K-Functional on Rotation Group SO(3)*

Zhuyuan Yang,Zongwen Yang

doi:10.4236/jamp.2017.52031

Abstract

In this paper we obtain the equivalence between modulus of smoothness and K-functional on rotation group SO(3).

Highlights

Many results of approximation are based on Euclid spaces or their compact subsets
Periodic approximation is based on compact group {exp(ix)}, whereas matrix group U(n) is the generalization of {exp(ix)}
Weyl proved the approximation theorem on compact group, that is, the irreducible character generate a dense subspace of the space of continuous classes function

Summary

Introduction

Many results of approximation are based on Euclid spaces or their compact subsets. Periodic approximation is based on compact group {exp(ix)}, whereas matrix group U(n) is the generalization of {exp(ix)}. Some approximation problems on compact groups have been studied since in 1920s F. Weyl proved the approximation theorem on compact group, that is, the irreducible character generate a dense subspace of the space of continuous classes function. Gongsheng (see [1]) studied the basic problems of Fourier analysis on unitary and rotation groups, including the degree of convergence of Abel sum based on Poisson kernel. We study the modulus of smoothness and K-functional on rotation group SO(3) and as classical casein Euclid space we will obtain the equivalence between them.

Dr g

We get