Math 139 Fourier Analysis Lecture 21: Steady-state heat equation in upper half plane, ct'd.

Mean value property of harmonic functions; uniqueness of solutions to steady-state heat equation on upper half plane. Poisson summation formula: periodization of a (Schwartz class) function; proof of summation formula; application of summation formula: heat kernel on the circle is the periodization of the heat kernel on the line.