Does it serve mainly as a narration or is there any substantive consequence which might not be derived without tools of functional analysis?
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$\begingroup$ This is an interdisciplinary site and here is a good interdisciplinary question, which should definitely stay open. $\endgroup$– Paul TaylorCommented May 3, 2015 at 9:56
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2$\begingroup$ @PaulTaylor the problem with the question is not that it is interdisciplinary, but that it is very vague, broad, and possibly opinion based. (Furthermore, the site is not really interdisciplinary it is, as its on-topic says, for research level math questions.) $\endgroup$– user9072Commented May 3, 2015 at 11:08
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$\begingroup$ @quid, I did mean to propose a soft question, and I thought research level math question could be a history topic. $\endgroup$– WfpiggieCommented May 3, 2015 at 13:33
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2$\begingroup$ Historical questions can be on-topic yet not if they are vague, broad, and possibly opinion based. $\endgroup$– user9072Commented May 3, 2015 at 13:36
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The theory of (unconditional and other) bases of Banach and Hilbert spaces has certainly played a role in the formulation of Gabor frames and bandwidth restricted frames in signal processing. And Fourier expansion served was a model.
answered May 3, 2015 at 11:01