Wavelets and Quasiasymptotics at a Point Original Research Article

Let {Vj, j∈Z} be a MRA of the spaceL2(R),ha tempered distribution, andhjits projection toVj,j∈Z. Then we prove that ifhhas the quasiasymptotic behavior at zero related to a regularly varying function, then so does eachhj,j∈Z, and also prove, with an additional condition, the opposite statement.