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Harinck, Pascale

Orbital functions on \(G_C/G_R\). Inversion formula of orbital integrals and Plancherel formula. (Fonctions orbitales sur \(G_C/G_R\). Formule d’inversion des intégrales orbitales et formule de Plancherel.) (French) Zbl 0899.22015

J. Funct. Anal. 153, No. 1, 52-107 (1998).
Author’s abstract: “Let \(G\) be a complex, connected and simply connected semisimple Lie group with Lie algebra \({\mathfrak g}\). Let \(H\) be a real form of \(G\) with Lie algebra \({\mathfrak h}\). After a general study of orbital functions on \(G/H\), we construct series of orbital functions which are eigen for the action of the \(G\)-invariant differential operators on \(G/H\). Using the results of [the author, J. Funct. Anal. 153, 1-51 (1998; preceding review)] about spherical generalized functions on \(G/H\), we prove the inversion formula for orbital integrals of \(C^\infty\)-functions with compact support on \(G/H\). We deduce the Plancherel formula for the symmetric space \(G/H\)”.
Reviewer: J.Ludwig (Metz)

Cited in 3 Documents

MSC:

22E46 Semisimple Lie groups and their representations
43A85 Harmonic analysis on homogeneous spaces

Keywords:

semisimple Lie group; real form; orbital functions; differential operators; spherical generalized functions; inversion formula; Plancherel formula; symmetric space
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\textit{P. Harinck}, J. Funct. Anal. 153, No. 1, 52--107 (1998; Zbl 0899.22015)
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