Notes on the Scaling Function

【摘要】：正 Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 a2,0 a2), then we havea1 ≤ 0, 0 b1, a1 b2/2 ≤ b1, 2π b2 - a1 ≤ 8π.