Self-adjoint Laplace operator with translation invariance on infinite-dimensional space \mathbb R^\infty

The standard Laplacian -\triangle_{\mathbb R^n} in L^2(\mathbb R^n) is self-adjoint and translation invariant on the finite-dimensional vector space \mathbb R^n. In this paper, using some quadratic form, we define a translation invariant operator -\triangle_{\mathbb R^\infty} on \mathbb R^\infty as a non-negative self-adjoint operator in some non-separable Hilbert space L^2(\mathbb R^\infty),... Show more