SU(2)上的Fourier级数的Gibbs现象

本文讨论了不可交换群SU(2)上的可积函数的Fourier级数及其Cesáro和的Gibbs现象。指出,当f(ρ,θ,ψ)∈L(SU(2))(这里,ρ,θ,ψ为SU (2)上的元素的Euler角)仅与θ,ρ有关时,在满足文中定理1的条件下,其Fourier级数在间断点上出现Gibbs现象。关于其Cesàro和,也有与古典的Fourièr级数类似的结果。

Gibbs's Phenomenon of Fourier Series on SU (2)

This paper discussed Gibbs's phenomenon of Fourier series on noncommutative group SU(2). If f(ρ,θ,ψ)is a function in L(SU(2))(whese ρ, θ、ψ are Euler's angles of the elements of SU(2)) depending only on θ and ρ, then under the condition of the Theorem 1, its Fourier series shows Gibbs's phenomenon in discontinuous points. About its Cesaro summation also has the same results as classical Fourier series.