TY - JOUR
T1 - On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$
AU - Dai , Shaoyu
AU - Liu , Yang
AU - Pan , Yifei
JO - Analysis in Theory and Applications
VL - 1
SP - 83
EP - 92
PY - 2023
DA - 2023/03
SN - 39
DO - http://doi.org/10.4208/ata.OA-2021-0027
UR - https://global-sci.org/intro/article_detail/ata/21463.html
KW - Laplace operator, polynomial, right inverse, weighted Hilbert space, Gaussian measure.
AB - <p style="text-align: justify;">Let $P(∆)$ be a polynomial of the Laplace operator $$∆ = \sum\limits^n_{j=1}\frac{∂^2}{∂x^2_j} \ \&nbsp; on&nbsp; \ \&nbsp; \mathbb{R}^n.$$ 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., $L^2(\mathbb{R}^n
,e^{−|x|^2}).$</p>