Dyadic Wavelet Frames

Abstract

In this chapter we consider dyadic wavelet frames, i.e., frames for L ²(ℝ) of the type {2^j/2 ψ(2^j x − k)} _{j, k∈ℤ}. Bases of this type were considered already in Section 3.8, where we also introduced the short notation {ψ _j,k } _j,k∈ℤ and {D ^j T _k ψ} _j,k∈ℤ. A frame of this type is said to be generated by ψ.