English

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 L2L^2-method, we study the operator kˉk+c\partial^k \bar{\partial}^{k} + c for any order kk in the weighted Hilbert space L2(C,ez2)L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2}). 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}
}