arrow
Volume 39, Issue 1
On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$

Shaoyu Dai, Yang Liu & Yifei Pan

Anal. Theory Appl., 39 (2023), pp. 83-92.

Published online: 2023-03

Export citation
  • 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., $L^2(\mathbb{R}^n ,e^{−|x|^2}).$

  • AMS Subject Headings

35A01, 35A25, 35D30, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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., $L^2(\mathbb{R}^n ,e^{−|x|^2}).$

Shaoyu Dai, Yang Liu & Yifei Pan. (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
Copy to clipboard
The citation has been copied to your clipboard