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On the relative fundamental solutions for a second order differential operator on the Heisenberg group

Volume 145 / 2001

T. Godoy, L. Saal Studia Mathematica 145 (2001), 143-164 MSC: Primary 43A80; Secondary 35A08. DOI: 10.4064/sm145-2-4

Abstract

Let $H_{n}$ be the $(2n+1)$-dimensional Heisenberg group, let $p,q\geq 1$ be integers satisfying $p+q=n$, and let $$ L=\sum _{j=1}^{p}( X_{j}^{2}+Y_{j}^{2}) -\sum _{j=p+1}^{n}(X_{j}^{2}+Y_{j}^{2}) , $$ where $\{ X_{1},Y_{1},\dots, X_{n},Y_{n},T\} $ denotes the standard basis of the Lie algebra of $H_{n}$. We compute explicitly a relative fundamental solution for $L$.

Authors

  • T. GodoyFacultad de Matematica, Astronomia y Fisica
    Universidad Nacional de Cordoba
    Ciudad Universitaria
    5000 Cordoba, Argentina
    e-mail
  • L. SaalFacultad de Matematica, Astronomia y Fisica
    Universidad Nacional de Cordoba
    Ciudad Universitaria
    5000 Cordoba, Argentina
    e-mail

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