### Abstract

We investigate properties of finite dimensional distributions of Brownian motion and other Levy processes which arose from our efforts to answer the following very "simple" question: What is the lowest eigenvalue for the rotationally invariant stable process in the interval (-1, 1)? While we still don't know the answer to this question, its investigation has led to interesting applications of finite dimensional distributions (multiple integrals) to eigenvalues and eigenfunctions of the Laplacian and "fractional" Laplacian.