Yoshiki AZUMA, Takashi ICHINOSE Note on Norm and Pointwise Convergence of Exponential Products and their Integral Kernels for the Harmonic Oscillator (73K, LaTeX2e) ABSTRACT. The aim of this paper is to study the exponential symmetric product formula for the semigroup of the one-dimensional harmonic oscillator to discuss its convergence pointwise of the integral kernels as well as in norm with sharp optimal error bound.