Say you wavelet transform a signal, multiply by some values, and untransform. Is there anything we can say about the effect in real space? I know that it's not exactly a convolution, because the convolution theorem doesn't really exist for the wavelet transform. So if it's not a convolution, what is it?
Also, is the effect different if you multiply in an orthogonal wavelet basis (at, say, dyadic frequencies) versus a continuous transform at all frequencies?