The Semigroup and the Inverse of the Laplacian on the Heisenberg Group

• APARAJITA DASGUPTA ^[1] ; M.W WONG ^[2]
  1. [1] Indian Institute of Science Department of Mathematics
  2. [2] York University Department of Mathematics and Statistics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 3, 2010, págs. 83-97
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000300006
• Enlaces
  • Texto completo
• Resumen
  • español

    Mediante descomposición del Laplaceano sobre el grupo de Heisenberg en una familia de operadores diferenciales parciales parametrizados Lt, t ∈ R \{0}, y usando transformada de Fourier-Wigner parametrizada, damos fórmulas y estimativas para la continuidad fuerte del semigrupo generado por Lt, y la inversa de Lt. Usando esas fórmulas y estimativas obtenemos estimativas de Sobolev para el semigrupo a un parámetro y la inversa del Laplaceano.

  • English

    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.

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