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> I find it funny how you think of differentiation in terms of "frequency domain", "bandlimit" and "filter". Very signal-processy, very engineery. A mathematician would speak about unbounded operators in a Banach space. :-)

This more or less depends on what kind of mathematician you're talking to. A mathematician working on Frames and signals almost certainly uses that language. But someone working in PDEs probably doesn't, even if the theory intersects a lot. It's probably a sign that there's nothing wrong with mathematicians and engineers sharing concepts :).



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