Wavelets Associated with Composite Dilations

1 Basic definitions In this paper, we present a description of a collaboration with K. Guo, W. Lim, A. Savov and E. Wilson. We make use of the Fourier transform f → ˆ f that, for f ∈ L 1 (R n), is defined asˆf (ξ) = R n f (x) e −2πiξx dx. As is well-known, this operator has a unique extension to L 2 (R n) that is a unitary operator. In the following, we refer to the domain ofˆf as the " frequency " domain and denote it by R n. The elements ξ ∈ R n will be denoted by Greek letters and considered to be row