How to prove the Parseval's identity , I know the formal way but how to justify the interchange between the integral and the sum in a rigorously way , in addition what extra condition does the function have to satisfy , is the continuity enough in this case ?
2026-04-26 02:42:22.1777171342
Parseval's identity
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Parseval's formula holds for every $L^2$-function, even if it's not continuous. You should be able to find the proof in any decent (sufficiently sophisticated) textbook on Fourier analysis.