Corrigendum to 'Bases of translates and multiresolution analyses' [Appl. Comput. Harmon. Anal. 24 (2008) 41–57]

Page Line Where it says Should say 42 8 f (x) := ∫ Rd e−i2π t·x f (t)dt f (x) := ∫ Rd e−i2πx·t f (t)dt 43 2 ψ(2x)= ei2πxμ(2x)p(2πx+ 1/2)φ(x) ψ(2x)= ei2πxμ(2x)p(x+ 1/2)φ(x) 43 17, 18 called Riesz sequence called a Riesz sequence 44 −9 L2(Rd L2(Rd) 45 −17 It follows that It follows from [25, Theorem 2.3.6] that 46 4 D1 = D1 (t)= 47 14 [1,n] × J I(n)× J 47 −21, −20 k is uniquely determined by j and r k uniquely determines j and r 47 −13 Theorem 3 yields Theorem 1(c) and Theorem 3 yield 49 19 T (u) S(u) 50 12 Note that Note that, except for a special case 51 −11 V j = r< j S(Ar;ψ) V j = ∑ r< j S(A r;ψ) 53 15 orthonormal basis orthonormal basis generator 53 −6 V(x) v(x) 54 4 V (x) := (v ,1(x), . . . , v ,|a|(x)) v (x) := (v ,1(x), . . . , v ,|a|(x)) 54 6 V (x) v (x) 54 −21 {μ1, . . . ,μn} {μ1, . . . ,μm} 54 −13 {μ1, . . . ,μn} {μ1, . . . ,μm} On page 49 line 1 and line −20, the expression “ψ = {ψ1, . . . ,ψr}” is redundant and should be deleted. On page 53 line −14, where it says V(x) := v1,1(x), . . . , v1,|a|(x), . . . , vn,1(x), . . . , vn,|a|(x) )T