This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein–Uhlenbeck semigroup e tL etL. Our approach is to expand the Mehler kernel into Hermite polynomials and apply the powers L N LN of the Ornstein–Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for L L. As an application we give an alternative proof of the kernel estimates by Ref. 10, making all relevant quantities explicit.
|Number of pages||13|
|Journal||Infinite Dimensional Analysis, Quantum Probability and Related Topics|
|Publication status||Published - 2016|
- Mehler kernel
- Gaussian measure
- Hermite polynomials
- Caldéron reproducing formula