Perturbation of Wavelet Frames of Quaternionic-Valued Functions - Fusheng Xiao; Jianxun He (Mathematics, 2021)
Let <semantics>L2(R,H)</semantics> denote the space of all square integrable quaternionic-valued functions. In this article, let <semantics>Φ∈L2(R,H)</semantics>. We consider the perturbation problems of wavelet frame <semantics>{Φm,n,a0,b0,m,n∈Z}</semantics> about translation parameter <semantics>b0</semantics> and dilation parameter <semantics>a0</semantics>. In particular, we also research the stability of irregular wavelet frame <semantics>{<msqrt>Sm</msqrt>Φ(Smx−nb),m,n∈Z}</semantics> for perturbation problems of sampling.