Wavelets and quasiasymptotics at a point (Q1288262)

Let \(\{V_j\), \(j \in {\mathbb Z}\}\) be a MRA of the space \(L^2({\mathbb R})\), \(h\) a tempered distribution, and \(h_j\) its projection to \(V_j\), \(j \in {\mathbb Z}\). The authors prove that if \(h\) has a quasiasymptotic behavior at zero related to a regularly varying function, then so does each \(h_j\), \(j \in {\mathbb Z}\), and also prove, with an additional condition, the converse statement.