Coefficients named for this person decay according to a power law whose degree is two plus the smoothness of the underlying function. This person’s namesake “extension” and “restriction” operators are the subject of the disproven Mizohata–Takeuchi conjecture. An overshoot of around 9 percent results from truncating constructs named for this person due to the Gibbs phenomenon. Constant functions become Dirac delta functions under an operation named for this person defined by integrating a function times “e to the minus i k x.” Periodic functions are decomposed into sums of trigonometric functions in this person’s namesake “series.” For 10 points, what mathematician names a transform that, like the Laplace transform, translates from the time domain to the frequency domain? ■END■
ANSWER: Joseph Fourier [accept Fourier series; accept Fourier transform; accept Fourier coefficients; accept Fourier restriction operator or Fourier extension operator]
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