ABSTRACT
In the previous chapter, we defined a fundamental solution for the exterior derivative operator d : D q ( ℝ N ) → D q + 1 ( ℝ N ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/in1847.tif"/> to be a kernel K ∈ D ′ N − 1 ( ℝ N × ℝ N ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/in1848.tif"/> which satisfies the equation d K = ( − 1 ) N [ Δ ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/equation992.tif"/> where d on the left is the exterior derivative on ℝ N × ℝ N , For a fundamental solution for the Cauchy–Riemann operator ∂ ¯ : D p , q ( ℂ n ) → D p , q + 1 ( ℂ n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/in1849.tif"/> , the analogous equation is ∂ ¯ K = [ Δ ] . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/equation993.tif"/>
