[FRIAM] Fourier image space, duality, filtering and compression

[Jon Zingale]

At today's zoom meeting, Barry mentioned something that I suspect was
interesting if I could have heard it. It was part of a larger point about,
perhaps, regretting not being introduced to Noether's theorem when learning
harmonic analysis. It reminded me of a question that Sarah asked me while
we were on vacation. She asked, "From what data did Heisenberg arrive at
his famous inequality? What physical experiment, if any, grounds the
result". Throughout the historical literature it is mentioned that he was
unaware of matrices and that eventually Max Born pointed out uncertainty as
a consequence of their non-commutativity. This got me wondering what
mathematical tools he did have in hand, what it was like back then to study
harmonic analysis outside of a linear algebraic context, as pure analysis?
Since Germany clearly voted Heisenberg "most likely to produce a nuclear
weapon", I have no doubt that he was very capable, but it does leave me
wondering what his intellectual process was like, what tools were in the
shed.
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