# Talk:Dirichlet kernel

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Field:  Analysis

Michael, in my field people refer to the entire collection as the Dirichlet kernel (that why you never hear the phrase "Dirichlet kernels"). I understand that each function is the kernel of the associated (finite dimensional range) convolution kernel. But each of these operators is not intersting in itself, only their collection is. Somehow in practice a kernel is always supposed to have some singularity. If its just a single function (say the Hilbert kernel) then the singularity is in the time domain. Here the singularity is in the "n domain", but other than the fact that one is discrete and the other is continuous, I don't see any significant difference.

Do you have some reference that refers to each function individually as a kernel?

Certainly. See the section titled "kernels of operators" in kernel (mathematics). Michael Hardy 16:28, 23 Jul 2004 (UTC)

As I said, this is all fine in a formal kind of way but when people in harmonic analysis talk about "the Dirichlet kernel", they mean the entire collection. Since the Dirichlet kernel is a topic in harmonic analysis, I think we should respect the standard in this field, not what somebody with a general functional analysis background would find natural. No?

Michael, since you didn't reply I'm going to revert this. If you still think I'm wrong, check first with a standard reference like Zygmund or Katznelson. Gadykozma 10:59, 29 Jul 2004 (UTC)

if someone could perhaps post a graph of the Dirichlet kernel, that would be helpful in understanding. Also, maybe a few references to its applications for windowing in signal processing would be useful.

Does anyone know how to prove the trig identity for dirichlet kernel without using complex exponentials? 129.173.119.74 (talk) 13:08, 5 March 2010 (UTC)

The obvious inductive argument works, though it's disgusting compared to just using the geometric series. 24.220.188.43 (talk) 07:44, 17 June 2011 (UTC)