Calculus for the Ambitious by T. W. Koerner, , T. W. K rner is Professor of Fourier Analysis in the Department of Pure. –, London Mathematical Society Lecture Note Series vol. T. W. Koerner (), Fourier Analysis, Cambridge: Cambridge University Press. A51, ()  T. W. Koerner, Fourier Analysis, Cambridge University Press ()  M. Hillery, R. F. O’Connell, M. O. Scully and E. P. Wigner, Phys.
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There is a proof of this identity in this answer. How do we justify the application of Fubini theorem t.w.koermer interchange the order of integration.
Exercises in Fourier Analysis (Electronic book text)
That was probably my answer you’re referring to, and I guess I didn’t furier the exact conditions the OP was stating too carefully. More general solutions were already given.
Thomas William Korner, Korner’s Korner, Pleasures of Counting, , Mathematics
I believe that the justification lies in the absolute convergence of each of the integrals in the double integral above, see T. Koerner, Fourier Analysis Secs. BTW I had occasion to use this result here: I updated my answer in the other thread.
It would probably have been a better idea to place a comment there. It was sheer luck that I saw this question. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
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