Displaying similar documents to “Solvability of second-order left-invariant differential operators on the Heisenberg group”

Solvability of invariant sublaplacians on spheres and group contractions

Fulvio Ricci, Jérémie Unterberger (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians L α on the spheres S 2 ⁢ n + 1 ≃ U ⁢ n + 1 / U ⁢ n . In the second part, we introduce a larger family of left-invariant sublaplacians L α , β on S 3 ≃ S ⁢ U ⁢ 2 and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.

Weyl algebra and a realization of the unitary symmetry

Strasburger, Aleksander

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In the paper the origins of the intrinsic unitary symmetry encountered in the study of bosonic systems with finite degrees of freedom and its relations with the Weyl algebra (1979, Jacobson) generated by the quantum canonical commutation relations are presented. An analytical representation of the Weyl algebra formulated in terms of partial differential operators with polynomial coefficients is studied in detail. As a basic example, the symmetry properties of the d -dimensional quantum...