Comment on 100 Years to Solve an Integral (2020)parentComments−fxj1yYes the dirac comb for example. Actually there are infinitely many.https://en.wikipedia.org/wiki/Dirac_comband for other:http://www.systems.caltech.edu/dsp/ppv/papers/journal08post/...−abetusk1yA question I hadn't even thought to ask, thanks.So, basically, the eigenfunctions of the Fourier transform are Hermite polynomials times a Gaussian [0] [1].[0] https://math.stackexchange.com/questions/728670/functions-th...[1] https://en.wikipedia.org/wiki/Hermite_polynomials#Hermite_fu...−perihelions1yAs well as the linear combinations (including infinite sums!) of Hermite functions with the same eigenvalue under the Fourier transform. (Those eigenvalues are infinitely degenerate). You could express sech(x) as such a sum.
Comments
Yes the dirac comb for example. Actually there are infinitely many.
https://en.wikipedia.org/wiki/Dirac_comb
and for other:
http://www.systems.caltech.edu/dsp/ppv/papers/journal08post/...
A question I hadn't even thought to ask, thanks.
So, basically, the eigenfunctions of the Fourier transform are Hermite polynomials times a Gaussian [0] [1].
[0] https://math.stackexchange.com/questions/728670/functions-th...
[1] https://en.wikipedia.org/wiki/Hermite_polynomials#Hermite_fu...
As well as the linear combinations (including infinite sums!) of Hermite functions with the same eigenvalue under the Fourier transform. (Those eigenvalues are infinitely degenerate). You could express sech(x) as such a sum.