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May 9, 2021 at 12:36 comment added Alexandre Eremenko V. Marchenko, Sturm-Liouville operators and their applications, Birkhauser, 1986.
May 9, 2021 at 9:59 comment added Jochen Glueck What you're asking for seems to be closely related to the so-called nuclear spectral theorem. But I'm very hesitant to call this an "answer" to your question, since most versions of the nuclear spectral theorem that I've seen left me with the feeling that, while they back up the intuition that "things are similar as for the Fourier transform", they are a much less powerful tool when it comes to really proving something.
May 8, 2021 at 20:55 history asked Ma Joad CC BY-SA 4.0