u(z) = ∫ P_r(θ-φ) g(e^{iφ}) dφ/(2π) gives harmonic extension to disk from boundary g. Poisson kernel P_r(θ) = (1-r²)/(1-2r cos θ + r²). Foundational for harmonic analysis on disk + Hardy space H².
u(z) = ∫ P_r(θ-φ) g(e^{iφ}) dφ/(2π) gives harmonic extension to disk from boundary g. Poisson kernel P_r(θ) = (1-r²)/(1-2r cos θ + r²). Foundational for harmonic analysis on disk + Hardy space H².