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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22964 |
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| _version_ | 1866908679939293184 |
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| author | Bodian, Eramane Ingoba, Winnie Ossete Sambou, Souhaibou Badiane, Papa Sambou, Salomon |
| author_facet | Bodian, Eramane Ingoba, Winnie Ossete Sambou, Souhaibou Badiane, Papa Sambou, Salomon |
| contents | By Hörmander's $L^2$-method, we study the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ for any order $k$ with $α, β, γ\in \mathbb{R}$ such that $(α, β, γ) \neq(0,0,0)$ 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 $α= γ=0$: The operator $β\bar{\partial}^{k} + c$ with $\vert β\vert \geq 1$. (2) Case where $β= γ=0$: The operator $α\partial^{k} \bar{\partial}^{k} + c$ with $\vert α\vert \geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized study of the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ in weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$ Bodian, Eramane Ingoba, Winnie Ossete Sambou, Souhaibou Badiane, Papa Sambou, Salomon Complex Variables By Hörmander's $L^2$-method, we study the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ for any order $k$ with $α, β, γ\in \mathbb{R}$ such that $(α, β, γ) \neq(0,0,0)$ 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 $α= γ=0$: The operator $β\bar{\partial}^{k} + c$ with $\vert β\vert \geq 1$. (2) Case where $β= γ=0$: The operator $α\partial^{k} \bar{\partial}^{k} + c$ with $\vert α\vert \geq 1$. |
| title | Generalized study of the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ in weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$ |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2511.22964 |