Abstract
We use a metaplectic operator to prove that the hierarchical twisted Laplacian L m is unitarily equivalent to the tensor product of the one-dimensional Hermite operator and the identity operator on L 2(ℝm+11), and we use this unitary equivalence to show that L m is globally hypoelliptic in the Schwartz space and in the Gelfand–Shilov spaces.
Mathematics Subject Classification (2010). Primary 47F05; Secondary 47G30.
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Molahajloo, S., Rodino, L., Wong, M.W. (2013). Metaplectic Equivalence of the Hierarchical Twisted Laplacian. In: Molahajloo, S., Pilipović, S., Toft, J., Wong, M. (eds) Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol 231. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0585-8_4
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DOI: https://doi.org/10.1007/978-3-0348-0585-8_4
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