Copy of Math 139 Fourier Analysis Lecture 22: Poisson summation formula

Poisson summation formula; heat kernel for the circle; relation with heat kernel on the line. Heat kernel on the circle is an approximation of the identity. Poisson kernel on the disc is the periodization of the Poisson kernel on the upper half plane. Digression into analytic number theory: theta function; functional relation for theta function; Theta function; digression: relation of theta, Riemann zeta, and Gamma functions. (Contrast +2)