The Existence Problem Of (A,Γ) Wavelets

Wavelet analysis is a new tool of time-frequency analysis besides Fourier analysis and Gabor analysis.It has been applied in signal processing,image processing and numerical analysis.A basic problem is which pairs of(A,Γ)exist wavelets, especially those which are extremely useful in practical applications.1.We have filled a gap using the techniques employed by Speegle,in Ionascu and Yang Wang's proof in the paper concerning the existence of single function wavelets,and settled the question in two-dimensional case.2.We give some new non-expansive matrices A and some latticesΓsuch that (A,Γ)single function wavelets exist.