Ciro Santilli @cirosantilli 40

Capoeira music is amazing. And some Brazilian pop adaptations of it have also been awesome.

The Fourier series of an $L^2$ function (i.e. the function generated from the infinite sum of weighted sines) converges to the function pointwise almost everywhere.

The theorem also seems to hold (maybe trivially given the transform result) for the Fourier series (TODO if trivially, why trivially).

Only proved in 1966, and known to be a hard result without any known simple proof.

This theorem of course implies that Fourier basis is complete for $L^2$, as it explicitly constructs a decomposition into the Fourier basis for every single function.

TODO vs Riesz-Fischer theorem. Is this just a stronger pointwise result, while Riesz-Fischer is about norms only?

One of the many fourier inversion theorems.

Some interesting analysis by Parth Shukla twitter.com/pparth | www.linkedin.com/in/parth-shukla-59583b20/:Apparently most of the routers were Chinese. No surprise there.

Some authors use the convention of:

Does deliver good concise ideas. Now we need something on the less concise side of it.

Nutrient that a given species cannot produce and must ingest in its diet.

But only for the proper Riemann integral: math.stackexchange.com/questions/2293902/functions-that-are-riemann-integrable-but-not-lebesgue-integrable

First publicly reached by Frontier.

The most notable exception is the borrowing of 3d-orbital electrons to 4s as in chromium, leading to a 3d5 4s1 configuration instead of the 3d4 4s2 we would have with the rule. TODO how is that observed observed experimentally?

Bibliography:

For a quick and dirty introduction to the format, see: ELF Hello World Tutorial.