@Article{ATA-39-1,
author = {Shaoyu, Dai and Yang, Liu and Yifei, Pan},
title = {On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$},
journal = {Analysis in Theory and Applications},
year = {2023},
volume = {39},
number = {1},
pages = {83--92},
abstract = {<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>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2021-0027},
url = {https://global-sci.com/article/73727/on-a-right-inverse-of-a-polynomial-of-the-laplace-in-the-weighted-hilbert-space-l2-mathbbrn-ex2}
}