Abstract
In a recent series of papers M.W. Wong has studied a degenerate elliptic partial differential operator related to the Heisenberg group. It turns out that Wong’s example is best understood when replaced in the context of the phase-space Weyl calculus we have developed in previous work; this approach highlights the relationship of Wong’s constructions with the quantum mechanics of charged particles in a uniform magnetic field. Using Shubin’s classes of pseudodifferential symbols we prove global hypoellipticity results for arbitrary phase-space operators arising from elliptic operators on configuration space.
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de Gosson, M. (2008). Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators. In: Rodino, L., Wong, M.W. (eds) New Developments in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 189. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8969-7_1
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DOI: https://doi.org/10.1007/978-3-7643-8969-7_1
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