Study of the operator $\partial^{k} \bar{\partial}^{k} + c$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$
Functional Analysis
2022-05-17 v1 Complex Variables
Abstract
By the H\"ormander's -method, we study the operator for any order in the weighted Hilbert space . We prove the existence of its right inverse witch is also a bounded operator.
Keywords
Cite
@article{arxiv.2205.07717,
title = {Study of the operator $\partial^{k} \bar{\partial}^{k} + c$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$},
author = {Eramane Bodian and Souhaibou Sambou and Papa Badiane and Winnie Ossete Ingoba and Salomon Sambou},
journal= {arXiv preprint arXiv:2205.07717},
year = {2022}
}