Some students have asked me about problem 2.13 in Mallat's book "A wavelet Tour of Signal Proccessing". After some work on it, I think is not completely correct. I think some hypostesis on modulus of continuity are needed.

I attach the statement.

Esentially, what it says, is that the convolution of a continuous and bounded variation function with a sinc converges UNIFORMLY to the function. I would need a kind of uniform Riemann-Lebesgue lemma to achieve that conclussion.

It is a relevant problem cause it could justify why we can truncate the spectrum of a signal and recover something not too diferent from that truncate spectra for L2 signals.

Let me know what do you think.

Thanks