• Suprio Bhar

Articles written in Proceedings – Mathematical Sciences

• Differential operators on Hermite Sobolev spaces

In this paper, we compute the Hilbert space adjoint $\partial^{*}$ of the derivative operator $\partial$ on the Hermite Sobolev spaces $\mathcal{S}_{q}$. We use this calculation to give a different proof of the ‘monotonicity inequality’ for a class of differential operators $(L, A)$ for which the inequality was proved in Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2(4) (2009) 515–591. We also prove the monotonicity inequality for $(L, A)$, when these correspond to the Ornstein–Uhlenbeck diffusion.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 4
September 2019