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Eramane Bodian

Publications and source records attributed to Eramane Bodian.

7 recordsLinked to original sources
arXiv2025

Generalized study of the operator $\alpha \partial^k \bar{\partial}^{k} + \beta \bar{\partial}^k +\gamma \partial^k + c$ in weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$

By H\"ormander's $L^2$-method, we study the operator $\alpha \partial^k \bar{\partial}^{k} + \beta \bar{\partial}^k +\gamma \partial^k + c$ for any order $k$ with $\alpha, \beta, \gamma \in \mathbb{R}$ such that $(\alpha, \beta, \gamma) \neq(0,0,0)$ in the weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$. We prove the existence of its right inverse which is also a bounded operator. Subsequently we will study two cases that arise from this operator, namely: (1) Case where $\alpha= \gamma=0$: The operator $\beta \bar{\partial}^{k} + c$ with $\vert \beta \vert \geq 1$. (2) Case where $\beta= \gamma=0$: The operator $\alpha \partial^{k} \bar{\partial}^{k} + c$ with $\vert \alpha \vert \geq 1$.

math.CV↗
arXiv2018

Résolution du $\partial\bar\partial$ pour les courants prolongeables définis dans un anneau

Dans ce papier, on résout d'abord le $\partial\bar\partial$ pour les courants prolongeables définis dans $\mathbb{C}^n$ privé d'une boule $B$ de $\mathbb{C}^n$, ensuite dans une variété analytique complexe contractile $X$, enfin on le résout pour un domaine $D=X\setminusΩ$, où $Ω$ est un domaine borné de $X$ défini par $\{z\in X\,\ /\,\ φ(z)<0\}$, (avec $φ$ une fonction d'exhaustion strictement plurisouharmonique). In this present paper, we first solve the $\partial\bar\partial$ for extendable currents definite in $\mathbb{C}^n\setminus B$, where $B$ is a ball of $\mathbb{C}^n$, then in a contractible analytic complex manifold $X$, and finally in a domain $D=X\setminusΩ$ where $Ω$ is a bounded domain of $X$ defined by $\{z\in X\,\ /\,\ φ(z)<0\}$, ($φ$ is an exhaution strictly plurisubharmonic function).

math.CV↗