Wavelets and Quasiasymptotics at a Point

Abstract

Let {V j ,j∈Z} be a MRA of the spaceL 2 (R),ha tempered distribution, andh j its projection toV j ,j∈Z. Then we prove that ifhhas the quasiasymptotic behavior at zero related to a regularly varying function, then so does eachh j ,j∈Z, and also prove, with an additional condition, the opposite statement. © 1999 Academic Press.