Characteristic functions of semigroups in semi-simple Lie groups

@article{Martin2019CharacteristicFO,
  title={Characteristic functions of semigroups in semi-simple Lie groups},
  author={L. A. S. San Martin and L. J. Santos},
  journal={Forum Mathematicum},
  year={2019},
  volume={31},
  pages={815 - 842}
}
Abstract Let G be a noncompact semi-simple Lie group with Iwasawa decomposition G = K ⁢ A ⁢ N {G=KAN} . For a semigroup S ⊂ G {S\subset G} with nonempty interior we find a domain of convergence of the Helgason–Laplace transform I S ⁢ ( λ , u ) = ∫ S e λ ⁢ ( 𝖺 ⁢ ( g , u ) ) ⁢ 𝑑 g {I_{S}(\lambda,u)=\int_{S}e^{\lambda(\mathsf{a}(g,u))}\,dg} , where dg is the Haar measure of G, u ∈ K {u\in K} , λ ∈ 𝔞 ∗ {\lambda\in\mathfrak{a}^{\ast}} , 𝔞 {\mathfrak{a}} is the Lie algebra of A and g ⁢ u = k ⁢ e… Expand
1 Citations
Flag Type of Semigroups: A Survey

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