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2019•arXiv (Cornell University)Open access

A right inverse of differential operator $\Delta+a$ in weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$

Shaoyu Dai, Yang Liu, Yifei Pan

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Abstract

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$.

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What this paper is about

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$.

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Available abstract

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$.

Key concepts: Differential operator, Inverse, Hilbert space, Mathematics, Differential (mechanical device), Operator (biology), Space (punctuation), Mathematical analysis

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A right inverse of differential operator $\Delta+a$ in weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$ — Research Paper | ScholarLens