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arXiv · 2205.07717

Study of the operator $\partial^{k} \bar{\partial}^{k} + c$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$

Eramane Bodian·Souhaibou Sambou·Papa Badiane·Winnie Ossete Ingoba·Salomon Sambou
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Abstract

By the H\"ormander's $L^2$-method, we study the operator $\partial^k \bar{\partial}^{k} + c$ for any order $k$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$. We prove the existence of its right inverse witch is also a bounded operator.

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Eramane Bodian, Souhaibou Sambou, Papa Badiane, Winnie Ossete Ingoba, Salomon Sambou. 2022-05-16. Study of the operator $\partial^{k} \bar{\partial}^{k} + c$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$. https://arxiv.org/abs/2205.07717

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