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Cubo (Temuco)

versión On-line ISSN 0719-0646


DASGUPTA, APARAJITA  y  WONG, M.W. The Semigroup and the Inverse of the Laplacian on the Heisenberg Group. Cubo [online]. 2010, vol.12, n.3, pp. 83-97. ISSN 0719-0646.

By decomposing the Laplacian on the Heisenberg group into a family of parametrized partial differential operators Lt ,t ∈ R \ {0}, and using parametrized Fourier-Wigner transforms, we give formulas and estimates for the strongly continuous one-parameter semigroup generated by Lt, and the inverse of Lt . Using these formulas and estimates, we obtain Sobolev estimates for the one-parameter semigroup and the inverse of the Laplacian.

Palabras clave : Heisenberg group; Laplacian; parametrized partial differential operators; Hermite functions; Fourier-Wigner transforms; heat equation; one parameter semigroup; inverse of Laplacian; Sobolev spaces.

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