I read that the Poisson Kernel for the upper half-plane, $K_y(x)=\frac{1}{\pi}\frac{y}{y^2+x^2}$ is an approximation to the identity. The text states this without proof and I am hoping to see a proof of this fact. Thank you in advance for the help.
2026-04-07 00:20:14.1775521214
Poisson Kernel in the upper half-plane is an identity approximation
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