(untitled) (Analysis in Theory and Applications, 2023)
Let P(∆) be a polynomial of the Laplace operator ∆ = ^n_j=1∂^2∂x^2_j on R^n. We prove the existence of a bounded right inverse of the differential operator P(∆) in the weighted Hilbert space with the Gaussian measure, i.e., L^2(R^n ,e^−|x|^2).