On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$
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@Article{ATA-39-83,
author = {Dai , ShaoyuLiu , Yang and Pan , Yifei},
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 = {
Let $P(∆)$ be a polynomial of the Laplace operator $$∆ = \sum\limits^n_{j=1}\frac{∂^2}{∂x^2_j} \ \ on \ \ \mathbb{R}^n.$$ 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., $L^2(\mathbb{R}^n ,e^{−|x|^2}).$
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0027}, url = {http://global-sci.org/intro/article_detail/ata/21463.html} }
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 -
Let $P(∆)$ be a polynomial of the Laplace operator $$∆ = \sum\limits^n_{j=1}\frac{∂^2}{∂x^2_j} \ \ on \ \ \mathbb{R}^n.$$ 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., $L^2(\mathbb{R}^n ,e^{−|x|^2}).$
Dai , ShaoyuLiu , Yang and Pan , Yifei. (2023). On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$.
Analysis in Theory and Applications. 39 (1).
83-92.
doi:10.4208/ata.OA-2021-0027
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