ABSTRACT
The general notion of a “frame” will enable us to present the continuous wavelet transform and its discretized version (to be studied later on) from a single functional-analytic viewpoint. The next two sections, 4.1 and 4.2, are essentially borrowed from [K], where this unified aspect of the two theories is described in a particularly lucid way. To summarize the general idea in a few lines: A frame is a collection a. := (at | l e I ) of vectors in a Hilbert space X that is rich enough to make sure that no vector x e X other than 0 is orthogonal to all aL. In the infinite dimensional case this is not so easy to guarantee. The aL need not be linearly independent, let alone orthonormal. As a consequence, frames are in general a “redundant” collection of vectors.
