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I believe i have been looking in the Internet once for the origin of the term "spectrum" in functional analysis and saw that the term was proposed by someone (by Hilbert?) with no relation to physics, but later by pure coincidence it turned out to be related to radiation spectrum in physics.

Is this really so? I would like to have some references about the origin of the term and about the possible relation of operator spectrum to radiation spectrum.

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    $\begingroup$ There is some information on this question here: mathoverflow.net/questions/9125/… $\endgroup$ – Paul Oct 15 '15 at 19:20
  • $\begingroup$ Indeed, but not very clear. $\endgroup$ – Alexey Oct 15 '15 at 19:41
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The terminology in math goes back to Hilbert, and the link to spectrum of atoms was indeed a coincidence. See section 7 of http://www.stolaf.edu/people/steen/Papers/73spectral.pdf, esp. the top of p. 369.

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    $\begingroup$ It is claimed here however that the term is due originally to Wirtinger (1897), and that "Wirtinger drew upon the similarity with the optical spectra of molecules when he used the term 'Bandenspectrum' with reference to Hill’s (differential) equation." $\endgroup$ – Alexey Oct 16 '15 at 13:42

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