3 ms·
Wow that was pretty mind-blowing. His Phi operator almost felt like he was doing some sort of "diagonalization" step of continuous derivatives/integrals into d
by sakras 4y ago
Wow that was pretty mind-blowing.
His Phi operator almost felt like he was doing some sort of "diagonalization" step of continuous derivatives/integrals into discrete differences/sums in the same way you would diagonalize a matrix.
I wonder if there's something there, maybe phi is some sort of analog to eigenvectors of integrals/derivatives.
- deleted 4y ago[deleted]
- dls2016 4y agoYeah, the Fourier transform diagonalizes differentiation. Or in other words "differentiation is a Fourier multiplier". Integration is like a low-pass filter (you divide by the amplitude of a component by its frequency and so higher frequencies get quieter) and differentiation is "noisy" since high frequency components get louder. d^2/dt^2(sin kt) = -k^2 sin(kt) This idea is used in the study of partial differential equations, especially dispersive. https://www.math.ucla.edu/~tao/preprints/chapter.pdf https://www.math.ucla.edu/~tao/preprints/chapter.pdf