Abstract
Let L and be the twisted Laplacian and its transpose, respectively, and let and , be the renormalization of these operators. Now, we define a new partial differential operator , , which will be called the generalized twisted bi-Laplacian of type (m, n) or simply, the twisted bi-Laplacian of type (m, n). The aim of this paper is to study some spectral properties of the generalized twisted bi-Laplacian . The essential self-adjointness and the global hypoellipticity in the Schwartz space, in the Gelfand–Shilov spaces and in terms of a new and suitable family of Sobolev spaces are also studied. Our approach is based on the paper “Spectral theory of the twisted bi-Laplacian” by Gramchev et al. [Arch Math. 2009;93:565–575].
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