On a Right Inverse of a Polynomial of the Laplace in the Weighted Hilbert Space $L^2 (\mathbb{R}^n ,e^{−|x|^2} )$
Year: 2023
Author: Shaoyu Dai, Yang Liu, Yifei Pan
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 1 : pp. 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., $L^2(\mathbb{R}^n ,e^{−|x|^2}).$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2021-0027
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 1 : pp. 83–92
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Laplace operator polynomial right inverse weighted Hilbert space Gaussian measure.