Btw Indeed I'm convinced that the fractional calculus will play a central role in obtaining not only a solution... I expect that many solutions will be found in the future... as with the theory of superfunctions... but in obtaining a naturalness criterion to such a solution.

I'm also excited because I feel like you are on something even if sometimes... I feel that you should focus more on some foundational chapter... like you did with the compositional integral. Probably I'm wrong since I bet most of the things you do are powered by 2+ centuries of standard and well known mathematical results... so I'm not going to doubt heavyweights as Legendre, Euler, Gauss, Riemann or Ramanujan anytime soon.

Last thing. Fourier transform. You know for sure that I'm totally ignorant in analysis: can't compute even the simpler integrals... maybe slowly I can compute antiderivatives of polynomials...

But Fourier transform must be something I can vaguely understand since I know from a lesson from Jacob Lurie about categorified Fourier theory. I'm not sure how it can help us but I'm sure that there is something deep about it since Lurie finds in it categorical beef. In fact at the end of the day he generalizes it to a transformation between actions of a group \(G\) into actions of character group \(G^\land\) of \(G\) (up to some complex detail). And all of this has to do with eigenvalues decomposition, spectra of operators and I bet, the essence of periodicity.

And since group actions are exactly what we call iterations groups... we see that there must be something boiling in the devil's kitchen. But it is early for me. I need to work more on the basics.

ADD: Another fascinating thing about Fourier stuff is that it seems to me it has to do with translating cartesian into polar.... from additive to multiplicative... from linear to circles...... Yea I need to study more.

I'm also excited because I feel like you are on something even if sometimes... I feel that you should focus more on some foundational chapter... like you did with the compositional integral. Probably I'm wrong since I bet most of the things you do are powered by 2+ centuries of standard and well known mathematical results... so I'm not going to doubt heavyweights as Legendre, Euler, Gauss, Riemann or Ramanujan anytime soon.

Last thing. Fourier transform. You know for sure that I'm totally ignorant in analysis: can't compute even the simpler integrals... maybe slowly I can compute antiderivatives of polynomials...

But Fourier transform must be something I can vaguely understand since I know from a lesson from Jacob Lurie about categorified Fourier theory. I'm not sure how it can help us but I'm sure that there is something deep about it since Lurie finds in it categorical beef. In fact at the end of the day he generalizes it to a transformation between actions of a group \(G\) into actions of character group \(G^\land\) of \(G\) (up to some complex detail). And all of this has to do with eigenvalues decomposition, spectra of operators and I bet, the essence of periodicity.

And since group actions are exactly what we call iterations groups... we see that there must be something boiling in the devil's kitchen. But it is early for me. I need to work more on the basics.

ADD: Another fascinating thing about Fourier stuff is that it seems to me it has to do with translating cartesian into polar.... from additive to multiplicative... from linear to circles...... Yea I need to study more.

MSE MphLee

Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)

S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)