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.KeywordsDegenerate elliptic operatorshypoellipticityphase space Weyl calculusShubin symbolsMathematics Subject Classification (2000)47F3035B6546F05
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