- #1

Wuberdall

- 34

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I have a problem that I am unable to resolve.

The sequence ##\{\mathrm{sinc}^n(x)\}_{n\in\mathbb{N}}## of positive integer powers of ##\mathrm{sinc}(x)## converges pointwise to the indicator function ##\mathbf{1}_{\{0\}}(x)##. This is trivial to prove, but I am struggling to decide if the convergence is uniform or not.

I hope that someone in here can help me, either by providing a reference or a sketch proof.

Thanks in regards.