Estimates of the smoothness of dyadic orthogonal wavelets of Daubechies type
Е. А. Родионов, Yu. A. Farkov · Mathematical Notes · 2009
Suppose that ω(φ, ·) is the dyadic modulus of continuity of a compactly supported function φ in L 2(ℝ+) satisfying a scaling equation with 2 n coefficients. Denote by α φ the supremum for values of α > 0 such that the inequality ω(φ, 2−j ) ≤ C2 −αj holds for all j ∈ ℕ. For the cases n = 3 and n = 4, we study the scaling functions φ generating multiresolution analyses in L 2(ℝ+) and the exact values of α φ are calculated for these functions. It is noted that the smoothness of the dyadic orthogonal wavelet in L 2(ℝ+) corresponding to the scaling function φ coincides with α φ .