Mar 6, 2025
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Basic schematic of Fourier transform spectroscopy with bandpass sampling (BPS-FTS) (Investigating the Influence of the Diffraction Effect on Fourier Transform Spectroscopy with Bandpass Sampling)
I wrote a crude parser for AsciiMath formulas to be able to get some Fourier series art from wolframalpha and draw them on oscillosope.
Here is the Konata Izumi-like curve :3 (not mine)
Test functions and [tempered] distributions require the notion of topological vector space … distributions can be traced back to Green's functions in the 1830’s to solve ordinary differential equations … the 1936 work of Sergei Sobolev on hyperbolic PDE’s.
Laurent Schwartz introduced the term "distribution" by analogy with a distribution of electrical charge, possibly including not only point charges but also dipoles and so on.
tempered distribution
topological vector space
(^ if there is a dipole, there must be a notion of subtraction, hence the need for a vector, and to speak of this very conceptually, use a TVS)