Heat equation and Schrödinger equation with translation invariance on the infinite-dimensional vector space ${\mathbb{R}}^{\infty }$

Hiroki Yagisita

The standard Laplacian $-{△}_{{\mathbb{R}}^n}$ in $L^2({\mathbb{R}}^n)$ is self-adjoint and translation invariant on the finite-dimensional linear space ${\mathbb{R}}^n$. In this pape…