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Commit 2022-05-27 19:20 41ca6015

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feat(analysis/convolution): The convolution of two functions (#13540)

  • Define the convolution of two functions.
  • Prove that when one of the functions has compact support and is C^n and the other function is locally integrable, the convolution is C^n.
  • Compute the total derivative of the convolution (when one of the functions has compact support).
  • Prove that when taking the convolution with functions that "tend to the Dirac delta function", the convolution tends to the original function.
  • From the sphere eversion project.

Estimated changes

added theorem convolution_assoc
added theorem convolution_congr
added theorem convolution_def
added theorem convolution_eq_right'
added theorem convolution_eq_swap
added theorem convolution_flip
added theorem convolution_lmul
added theorem convolution_lmul_swap
added theorem convolution_lsmul
added theorem convolution_lsmul_swap
added theorem convolution_smul
added theorem convolution_zero
added theorem dist_convolution_le'
added theorem dist_convolution_le
added theorem smul_convolution
added theorem zero_convolution