The semigroup and the inverse of the Laplacian on the Heisenberg group

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DOI:

https://doi.org/10.4067/S0719-06462010000300006

Abstract

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

Keywords

Heisenberg group , Laplacian , parametrized partial differential operators , Hermite functions , Fourier-Wigner transforms , heat equation , one parameter semigroup , inverse of Laplacian , Sobolev spaces
  • Aparajita Dasgupta Department of Mathematics, Indian Institute of Science, Bangalore–560012, India.
  • M.W. Wong Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada.
  • Pages: 83–97
  • Date Published: 2010-10-01
  • Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal

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Published

2010-10-01

How to Cite

[1]
A. Dasgupta and M. Wong, “The semigroup and the inverse of the Laplacian on the Heisenberg group”, CUBO, vol. 12, no. 3, pp. 83–97, Oct. 2010.

Issue

Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal

Section

Articles