ABSTRACT
The classical continuous wavelet transform for functions on R is an integral
transform for which the kernel is the dilated translate of a so-called wavelet g, a quite
arbitrary square integrable function on R. A Plancherel formula for this transform is
obtained, and in the course of its derivation we naturally arrive at an admissibility
assumption for the wavelet g. There follow a Parseval and a pointwise reconstruction
formula
In this chapter, using the paper [52] we give whithout proofs the main results or
the classical wavelets on [0, + <»[, and on the classical wavelet transform on [0, »[.
