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Study of the operator $\partial^{k} \bar{\partial}^{k} + c$ in the weighted Hilbert space $L^2(\mathbb{C}, {\rm e}^{-\vert z \vert^2})$ (2205.07717v1)

Published 16 May 2022 in math.FA and math.CV

Abstract: By the H\"ormander's $L2$-method, we study the operator $\partialk \bar{\partial}{k} + c$ for any order $k$ in the weighted Hilbert space $L2(\mathbb{C}, {\rm e}{-\vert z \vert2})$. We prove the existence of its right inverse witch is also a bounded operator.

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