Characteristic functions of semigroups in semi-simple Lie groups

Autor(es)

San Martin, Luiz A. B. ^[1] ; Santos, Laercio J. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Math, Campinas, SP - Brazil

^[2] Univ Fed Juiz de Fora, Dept Math, Juiz De Fora, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: FORUM MATHEMATICUM; v. 31, n. 4, p. 815-842, JUL 2019.
• Citações Web of Science: 0

Resumo

Let G be a noncompact semi-simple Lie group with Iwasawa decomposition G = KAN. For a semigroup S subset of G with nonempty interior we find a domain of convergence of the Helgason - Laplace transform I-s(lambda, u) = integral(S)e(lambda(a(g,u))) dg, where dg is the Haar measure of G, u is an element of K, lambda is an element of a{*}, a is the Lie algebra of A and gu = ke(a(g,u))n is an element of KAN. The domain is given in terms of a flag manifold of G written F-Theta(s) called the flag type of S, where Theta(S) is a subset of the simple system of roots. It is proved that I-S(lambda,u) < infinity if lambda belongs to a convex cone defined from Theta(S) and u is an element of pi(-1)(D-Theta(s)(S)), where D-Theta(s)(S) subset of F-Theta(s) is a B-convex set and pi : K -> F-Theta(s) is the natural projection. We prove differentiability of 1 5 (A, u) and apply the results to construct of a Riemannian metric in D-Theta(s)(S) invariant by the group S boolean AND S(-1 )of units of S. (AU)

• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático