Construction of minimum-energy multiwavelets frames with dilation factor 3

In this paper, we study minimum-energy multi-wavelets frames Ψ = {ψ
¹
, ψ
²
, …, ψ
^N
} with dilation factor 3 for L
²
(R), Ψ correspond to some refutable functions with compact support. Firstly, the concept of minimum-energy multi-wavelets frames is generalized to dilation factor 3 and a precise characterization of Ψ is given in terms of the Laurent matrix polynomial of the refinable functions. Secondly, a necessary condition and some sufficient conditions are given. Finally, we present a numerical example.